problem solving multiple step problems practice 2 7 answers

Two-Step Equations Exercises

Two-step equations practice problems with answers.

Hone your skills in solving two-step equations because it will serve as your foundation when solving multi-step equations. I prepared eight (8) two-step equations problems with complete solutions to get you rolling.

My advice is for you to solve them by hand using a pencil or pen and paper. Believe me, you get the most benefit from this exercise by doing it yourself first before looking at the solution set.

If by any chance you get stuck or don’t know what to do next, please feel free to review my other lesson about two-step equations. Click the link below to get there. Enjoy!

Solving Two-Step Equations

1) Solve the two-step equation for [latex]g[/latex].

[latex]2g – 4 = 6[/latex]

Add both sides by [latex]4[/latex] then divide both sides by [latex]2[/latex].

2) Solve the two-step equation for [latex]x[/latex].

[latex]2x + 15 = – 3x[/latex]

Subtract both sides by [latex]2x[/latex]. Finally, divide both sides of the equation by [latex]-5[/latex].

3) Solve the two-step equation for [latex]k[/latex].

[latex]{\Large{{k \over 4}}} – 7 = – 5[/latex]

Add both sides by [latex]7[/latex]; followed by multiplying both sides by [latex]4[/latex].

4) Solve the two-step equation for [latex]m[/latex].

[latex]{\Large{{{m + 9} \over 5}}} = {\large{2}}[/latex]

Multiply [latex]5[/latex] on both sides then subtract by [latex]9[/latex] on both sides of the equation as well.

5) Solve the equation for [latex]y[/latex].

[latex]0 = – 1 – y[/latex]

Add [latex]1[/latex] to both sides of the equation. Notice that the coefficient of [latex]-y[/latex] is [latex]-1[/latex]. That means, we should divide both sides by [latex]-1[/latex] to isolate and therefore solve for [latex]y[/latex].

6) Solve the equation for [latex]r[/latex].

[latex] – 3\left( {r – 7} \right) = – 24[/latex]

First, divide both sides of the equation by [latex]-3[/latex] then add by [latex]7[/latex].

7) Solve the equation for [latex]z[/latex].

[latex]{\Large{5 \over 4}}z + {\Large{3 \over 4}}z = 1[/latex]

8) Solve the equation for [latex]x[/latex].

[latex]4.25 – 0.25x = 3.75[/latex]

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These free  equations and word problems   worksheets  will help your students practice writing and solving equations that match real-world story problems.

These free algebra worksheets are printable and available in a variety of formats.  Of course, answer keys are provided with each free algebra worksheet.

Equations and Word Problems (Two Step Equations) Worksheet 1  – This 10 problem worksheet will help you practice writing and solving two step equations that match real world situations. Equations and Word Problems (Two Step Equations) Worksheet 1 RTF  Equations and Word Problems (Two Step Equations) Worksheet 1 PDF  Preview Equations and Word Problems Worksheet 1 In Your Web Browser  View Answers

Equations and Word Problems (Two Step Equations) Worksheet 2  – This 10 problem worksheet will help you practice writing and solving two step equations that match real world situations. Equations and Word Problems (Two Step Equations) Worksheet 2 RTF  Equations and Word Problems (Two Step Equations) Worksheet 2 PDF  Preview Equations and Word Problems Worksheet 2 In Your Web Browser  View Answers

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Easy Multi-Step Word Problems

Welcome to The Easy Multi-Step Word Problems Math Worksheet from the Word Problems Worksheets Page at Math-Drills.com. This math worksheet was created or last revised on 2017-04-26 and has been viewed 1,054 times this week and 1,054 times this month. It may be printed, downloaded or saved and used in your classroom, home school, or other educational environment to help someone learn math.

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Use the buttons below to print, open, or download the PDF version of the Easy Multi-Step Word Problems math worksheet . The size of the PDF file is 55615 bytes . Preview images of the first and second (if there is one) pages are shown. If there are more versions of this worksheet, the other versions will be available below the preview images. For more like this, use the search bar to look for some or all of these keywords: math, word, problems, multi-step, addition, subtraction, multiplication, division .

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• Two-step equations – word problems

Simply put, two-step equations – word problems are two step equations expressed using words instead of just numbers and mathematical symbols. They are just a bit more complicated than one-step equations with word problems and they demand just a bit more effort to solve. If you are not confident in your abilities to solve two-step equations with word problems, you can go to one-step equations – word problems and practice some more before continuing with this lesson. But if you feel ready, we will show you how to solve it using this example:

Hermione’s Bikes rents bikes for $10 plus $4per hour. Janice paid $30 to rent a bike. For how many hours did she rent the bike?

First thing we have to do in this assignment is to find the variable and see what its connection is with the other values. The thing we do not know is the number of hours Janice rented the bike for and we have been asked to find that out. That means the number of hours is our variable.

The cost of renting a bike is 10$ to take the bike and 4$ for every hour it spends in our possession. The final sum Janice paid is $30. Let us write that down as an equation.

4 * x + 10 = 30

Now, in order to make things neater and more clear, let us move all the numbers (except for the number 4 – we have to get rid of it in a different way) to the right side of the equation. Like this:

4 * x = 30 – 10

To simplify things further, let us perform the subtraction.

The next thing to do is to get rid of the number 4 in front of the variable. We will do that by dividing the whole equation by 4.

4 * x = 20 |:4

Now that we have calculated the value of the variable, we can tell that Janice rented that bike for 5 hours. If you want to check the result – you can. If you multiply $4 that Janice paid per hour by the 5 hours she spend with that bike and then add the $10 she had to pay regardless of the time she spent with the bike, you will get a total sum of $30 that is indeed the full sum she paid.

These word problems are called two-step because you have to perform two mathematical operations in order to solve them. In this case – addition (subtraction) and multiplication (division). To practice solving two-step equations – word problems, feel free to use the worksheets below.

Two-step equations – word problems exams for teachers

Two-step equations – word problems worksheets for students

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Multi-Step Equation Worksheets

A huge collection of printable multi-step equations worksheets involving integers, fractions and decimals as coefficients are given here for abundant practice. Solving and verifying equations, applications in geometry and MCQs are included in this section for 7th grade and 8th grade students. We offer some free worksheets too!

Solving Equations Involving Integers: Level 1

In these 'Level 1' worksheets, solve each multi-step equation to find the value of the unknown variable. Five exclusive pdfs are here for practice.

• Download the set

Solving Equations Involving Integers: Level 2

These 'Level 2' multi-step equations may involve a few more steps to arrive the solution than level 1. A plenty of practice worksheets are available here.

Solving Equations Involving Fractions

These printable worksheets have equations whose coefficients are fractions and integers. Solve each multi-step equation. Eight questions are given per worksheet.

Solving Equations Involving Decimals

In these pdf worksheets for grade 7 and grade 8, perform the basic arithmetic operation and solve the multi-step equations having decimal numbers as coefficients.

Solving Equations: Mixed Review

A combination of integer, fraction and decimal coefficients stands for the variable in these mixed review worksheets. Practice them all.

Equation Word Problems Worksheets

Read the word problems and write down the equations. Solve them in one, two or more steps to find the solution.

(30 Worksheets)

Solve and Verify the Solution

In these pdf worksheets, solve the multi-step equations and verify your solution by substituting the value of the unknown variable to the equation.

Translating Multi-Step Equation

Translate the given phrases to algebraic equations. Three exclusive practice sheets are available here for students.

Equations in Geometry: Type 1

Nine geometric shapes are shown in each worksheet. Their sides are given in the form of expressions. Solve them to find the unknown variable.

Area and Perimeter - Shapes: Type 2

In these printable worksheets, the area and perimeter of nine shapes are given. Use the given expressions and apply the area and perimeter formula to solve them.

Equations in Geometry: Type 3

A collection of word problems involving properties of shapes are given. Set up the equation and solve each multi-step equation.

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Two-step word problems.

Two-step word problems have three numbers which must be operated on separately, and in the right order. They take much more understanding of the problem than simple word problems because they provide the information in a less structured form.

• Addition, then Subtraction
• Addition, then Multiplication
• Addition, then Division
• Subtraction, then Addition
• Subtraction, then Multiplication
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Multi-Step Problem Solving Worksheet

Updated:  23 Jun 2023

Solve a multi-step problem and explain the mathematical reasoning behind the process with this simple assessment worksheet.

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Non-Editable:  PDF

Pages:  1 Page

• Curriculum Curriculum:  CCSS, TEKS

Grades:  2 - 3

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CCSS.MATH.CONTENT.2.OA.A.1

Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with...

CCSS.MATH.CONTENT.3.OA.D.8

Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including roundi...

Math 2.4(C)

Solve one-step and multi-step word problems involving addition and subtraction within 1,000 using a variety of strategies based on place value, including algorithms; and

Math 3.4(A)

Solve with fluency one-step and two-step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction;

This worksheet is best used as independent practice for your problem-solving  lesson.

Students read the multi-step problem, then use an appropriate strategy of their choosing to calculate the answer. Space is provided on the worksheet for students to explain the steps they took to solve the problem.

Multi-Step Problem Solving Worksheet: Scaffolding & Extension Tips 

In addition to individual student work time, use this mathematics worksheet as a:

• Post-lesson exit ticket  
• Homework assignment
• Whole-class review (via smartboard)

Got fast finishers ? Encourage students who require an additional challenge to write their own multi-step problem for a partner to solve.

Some students become overwhelmed when confronted with multi-step word problems. It is important to support these students to break the problem down into smaller segments. Have them highlight the key information in the problem. Some students may find it helpful to use a problem-solving mat to organize this information and to plan their approach.

A Variety of Ways to Prepare This Resource

Because this resource includes an answer sheet, we recommend you print one copy of the entire file. Then, make photocopies of the blank worksheet for students to complete.  

You can also turn this teaching resource into a sustainable activity! Print a few copies on cardstock and slip them into dry-erase sleeves. Students can record their answers with a dry-erase marker, then erase and reuse. 

Additionally, project the worksheet onto a screen and work through it as a class by having students record their answers in their notebooks.

Before You Download

Use the dropdown icon on the Download button to choose between the PDF or Google Slides version of this resource. An answer key is also included with this download.

This resource was created by  Allie Kleijnjans, a teacher in Pennsylvania and Teach Starter Collaborator. 

Don’t stop there! We’ve got more activities to help you cut down on lesson planning time:  

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Doubles to Twenty

A set of 20 posters to help students remember double numbers to ten.

Doubles Plus 1 - Game Boards

30 game boards to use when practicing the doubles plus one strategy with single and double-digit numbers.

Doubles Minus 1 - Game Boards

30 game boards to use when practicing the doubles minus one strategy with single and double-digit numbers.

Doubles Minus One - Dice Roll Worksheet

Practice the doubles minus one addition strategy with this one-page worksheet.

Doubles Plus One - Dice Roll Worksheet

Practice the doubles plus one addition strategy with this one-page worksheet.

Doubles Minus One - Grid Game

Practice the doubles minus one addition strategy with this dice game.

Doubles Plus One - Grid Game

Practice the doubles plus one addition strategy with this dice game.

Doubles Minus One - Worksheet

Doubles Plus One - Worksheet

Double Bubble – Doubling Game

Practice the doubles addition strategy with this fun board game.

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Free Printable Multi-Step Word Problems worksheets

Multi-Step Word Problems: Discover a vast collection of free printable math worksheets, crafted by expert educators to help students develop problem-solving skills and master complex mathematical concepts. Ideal for teachers and learners alike!

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Explore printable Multi-Step Word Problems worksheets

Multi-Step Word Problems worksheets are an essential tool for teachers looking to challenge their students in the realm of Math. These worksheets provide a variety of Math Word Problems that require students to use critical thinking and problem-solving skills to find the solution. By incorporating multiple steps, these worksheets help students develop a deeper understanding of mathematical concepts and improve their ability to apply these concepts in real-world situations. Teachers can use these worksheets to create engaging and interactive lessons, allowing students to work individually or in groups to solve the problems. With a wide range of topics and difficulty levels, Multi-Step Word Problems worksheets cater to the diverse needs of students and can be easily adapted to suit different grade levels.

Quizizz is an excellent platform for teachers to access a vast library of worksheets, including Multi-Step Word Problems worksheets, and other valuable resources for teaching Math. With Quizizz, teachers can create customized quizzes and interactive lessons that incorporate Math Word Problems, allowing students to practice and improve their problem-solving skills. The platform also offers various features such as real-time feedback, progress tracking, and gamification elements, making learning Math more engaging and enjoyable for students. Teachers can easily integrate Quizizz into their lesson plans, ensuring that students receive a comprehensive and well-rounded education in Math. By utilizing Quizizz and its extensive collection of worksheets, teachers can effectively teach Math Word Problems and help their students excel in this crucial subject.

Solving Multi-Step Equations

Andymath.com features free videos, notes, and practice problems with answers! Printable pages make math easy. Are you ready to be a mathmagician?

Practice Problems

Solve for x, \(\textbf{1)}\) \(3x+2=14\) show answer the answer is \(x=4\), \(\textbf{2)}\) \(5x-2=8\) show answer the answer is \(x=2\), \(\textbf{3)}\) \(\displaystyle\frac{x}{3}-7=2\) show answer the answer is \(x=27\), \(\textbf{4)}\) \(\displaystyle\frac{x}{5}+2=4\) show answer the answer is \(x=10\), \(\textbf{5)}\) \(\displaystyle\frac{x+2}{3}=2\) show answer the answer is \(x=4\), \(\textbf{6)}\) \(\displaystyle\frac{x-4}{5}=2\) show answer the answer is \(x=14\), \(\textbf{7)}\) \(3x+5=7x-3\) show answer the answer is \(x=2\), \(\textbf{8)}\) \(2x-1=4x-5\) show answer the answer is \(x=2\), \(\textbf{9)}\) \(\displaystyle\frac{x}{5}+\displaystyle\frac{x}{6}=11\) show answer the answer is \(x=30\), \(\textbf{10)}\)\(\displaystyle\frac{x}{2}+\displaystyle\frac{x}{3}=5\) show answer the answer is \(x=6\), \(\textbf{11)}\) \(4− (2− 3x) = 9\) show answer \(x = \displaystyle\frac{7}{3}\) show work \(4+ -1(2− 3x) = 9 \,\,\,\) (rewrite to clarify) \(4 -2 + 3x = 9 \,\,\,\) (distribute the -1) \(2 + 3x = 9 \,\,\,\) (simplify) \(3x = 7 \,\,\,\) (subtract 2 from both sides) \(x = \displaystyle\frac{7}{3} \,\,\,\) (divide both sides by 3), \(\textbf{12)}\) \(3(2x+5)-4(x-1)=23\) show answer the answer is \(x=2\), \(\textbf{13)}\) \(2(3x+5)-3(4x-3)=13\) show answer the answer is \(x=1\), \(\textbf{14)}\) \(2x-5=10\) show answer the answer is \(x=7.5\) or \(7 \frac{1}{2}\), challenge problems, solve for z, \(\textbf{15)}\) \(zx+ry=n\) show answer the answer is \(z=\displaystyle\frac{n-ry}{x}\), \(\textbf{16)}\) \(zx+zny=m\) show answer the answer is \(z=\displaystyle\frac{m}{x+ny}\), see related pages\(\), \(\bullet\text{ equation calculator }\) \(\,\,\,\,\,\,\,\,\text{(symbolab.com)}\), \(\bullet\text{ equation solver calculator (symbolab.com)}\) \(\,\,\,\,\,\,\,\,2x+5=11…\), \(\bullet\text{ solving equations by addition and subtraction}\) \(\,\,\,\,\,\,\,\,x+3=4…\), \(\bullet\text{ solving equations by multiplication and division}\) \(\,\,\,\,\,\,\,\,8x=48…\), \(\bullet\text{ solving multi-step equations}\) \(\,\,\,\,\,\,\,\,3x+2=14…\), \(\bullet\text{ solving equations with variables on both sides}\) \(\,\,\,\,\,\,\,\,3x+5=7x-3…\), \(\bullet\text{ solving equations with decimals}\) \(\,\,\,\,\,\,\,\,43.5+0.2x=51.1…\), \(\bullet\text{ solving equations with fractions}\) \(\,\,\,\,\,\,\,\,\frac{2}{5}x+\frac{2}{3}=\frac{8}{3}…\), \(\bullet\text{ andymath homepage}\).

Solving equations involves finding the value of a variable by manipulating and rearranging algebraic equations with multiple steps. These equations typically have multiple terms on one or both sides of the equal sign and may involve the use of the distributive property and combining like terms. Learning about solving equations is important because it helps us understand how to solve real-world problems involving algebra. It also helps us develop critical thinking and problem-solving skills, which are valuable in many different fields.

Real world examples of solving equations, a carpenter is building a bookshelf that is 8 feet long. the carpenter wants to divide the bookshelf into 3 equal sections. how long should each section be a store is selling bags of apples for $4 each. if a customer buys 7 bags, how much will they spend in total a runner runs a total of 20 miles in 5 days. on average, how many miles does the runner run per day a swimmer swims a total of 50 laps in a pool that is 25 meters long. how far did the swimmer swim in total a baker needs to bake a cake that serves 12 people. if the baker only has enough ingredients to make a cake that serves 9 people, how much more of each ingredient does the baker need to buy, about andymath.com, andymath.com is a free math website with the mission of helping students, teachers and tutors find helpful notes, useful sample problems with answers including step by step solutions, and other related materials to supplement classroom learning. if you have any requests for additional content, please contact andy at [email protected] . he will promptly add the content. topics cover elementary math , middle school , algebra , geometry , algebra 2/pre-calculus/trig , calculus and probability/statistics . in the future, i hope to add physics and linear algebra content. visit me on youtube , tiktok , instagram and facebook . andymath content has a unique approach to presenting mathematics. the clear explanations, strong visuals mixed with dry humor regularly get millions of views. we are open to collaborations of all types, please contact andy at [email protected] for all enquiries. to offer financial support, visit my patreon page. let’s help students understand the math way of thinking thank you for visiting. how exciting.

Printable Multi-step Word Problems for 2nd Graders

Are you looking to boost your child's problem-solving skills? Our multi-step word problems worksheets for 2nd graders are designed to enhance critical thinking and mathematical reasoning. These worksheets cover a variety of skills including addition, subtraction, and logical sequencing. With engaging themes l ... Read more ike seasonal and holiday-themed problems, your child will enjoy learning. Perfect for building a strong foundation in math. Start now for free!

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Add Using Part-Part-Whole Model Worksheet

Dive into this fun-filled printable worksheet by practicing to add using 'Part-Part-Whole' model.

Solve Two-Step Word Problems on Same Operation Worksheet

Make math practice a joyride by solving two-step word problems on the same operation.

Solve Two-Step Story Problems on Same Operation Worksheet

Assess your math skills by solving two-step story problems on the same operation.

Solving Mystery Problems on Same Operation Worksheet

Put your skills to the test by solving mystery problems on the same operation.

Model and Solve Mystery Problems on Same Operation Worksheet

Use this printable worksheet to model and solve mystery problems on the same operation.

Solve Two-Step Word Problems on Add & Subtract Worksheet

In this worksheet, learners will get to solve two-step word problems on addition & subtraction.

Solve Two-Step Story Problems on Add & Subtract Worksheet

Become a mathematician by solving two-step story problems on addition & subtraction.

Solving Mystery Problems on Add & Subtract Worksheet

Boost your math skills by solving mystery problems on addition & subtraction.

Model and Solve Mystery Problems on Add & Subtract Worksheet

Focus on core math skills by modeling and solving problems on addition & subtraction.

Comparison Word Problems Using Bar Model Worksheet

Assess your math skills by comparing word problems using bar model in this worksheet.

Add and Subtract within 10: Summer Word Problems Worksheet

Summer-themed worksheet focusing on solving word problems involving addition and subtraction within 10.

Add and Subtract within 20: Summer Word Problems Worksheet

Engage with this summer-themed worksheet to practice addition and subtraction within 20 through word problems.

Add and Subtract within 10: Halloween Word Problems Worksheet

Spooky worksheet to practice adding and subtracting within 10 using Halloween-themed word problems.

Add and Subtract within 20: Halloween Word Problems Worksheet

Engaging Halloween-themed worksheet to hone students' skills in adding and subtracting within 20.

Add and Subtract within 10: Christmas Word Problems Worksheet

Engaging Christmas-themed worksheet on adding and subtracting within 10, featuring word problems.

Add and Subtract within 20: Christmas Word Problems Worksheet

Engaging Christmas-themed worksheet focused on enhancing addition and subtraction skills within 20.

Add and Subtract within 10: Shopping Word Problems Worksheet

Engaging worksheet to practice addition and subtraction within 10 using fun shopping scenarios.

Add and Subtract within 20: Shopping Word Problems Worksheet

This worksheet helps students practice addition and subtraction within 20 using a fun shopping theme.

Add and Subtract within 10: Travel Word Problems Worksheet

Engaging travel-themed worksheet to enhance students' skills in adding and subtracting within 10.

Add and Subtract within 20: Travel Word Problems Worksheet

Travel-themed worksheet for mastering addition and subtraction within 20 through word problems.

Add and Subtract within 10: Cooking Word Problems Worksheet

Whip up math skills with this cooking-themed worksheet on adding and subtracting within 10!

Add and Subtract within 20: Cooking Word Problems Worksheet

Engage in this cooking-themed worksheet that hones your skills in adding and subtracting within 20!

Add and Subtract within 10: Winter Word Problems Worksheet

Winter-themed worksheet for students to solve word problems using addition and subtraction within 10.

Add and Subtract within 20: Winter Word Problems Worksheet

Engaging winter-themed worksheet to sharpen skills in adding and subtracting within 20!

Add and Subtract within 10: Easter Word Problems Worksheet

Easter-themed worksheet for students to practice adding and subtracting numbers within 10.

Add and Subtract within 20: Easter Word Problems Worksheet

Easter-themed worksheet for students to solve addition and subtraction problems within 20.

Add and Subtract within 10: Thanksgiving Word Problems Worksheet

Thanksgiving-themed worksheet for students to practice adding and subtracting within 10.

Add and Subtract within 20: Thanksgiving Word Problems Worksheet

Engaging Thanksgiving-themed worksheet to practice addition and subtraction within 20.

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Assignment_return worksheet: solving multi-step problems standard(s): 7.ee.b.3.

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Choose another grade, jennifer has $1.25 in nickels. how many nickels does she have, before $.noconflict(true), standard: 7.ee.b.3, domain: expressions & equations, theme: solve real-life and mathematical problems using numerical and algebraic expressions and equations, description: solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. apply properties of operations as strategies to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. for example: if a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. if you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation., kate is one year and six months younger than her sister. if her sister is 14 years and 2 months old, how old is kate, 12 years, 0 months, 13 years, 2 months, 12 years, 8 months, 14 years, 0 months, bob, the plumber, charges 1 4 the cost of materials as his labor fee. if his current job has a material cost of $130, how much will bob charge his client (including his labor fee), none of the above, when lana awoke this morning, she turned on the tv and learned that the outdoor temperature was a chilly 0 degrees celsius. if she was talking to a friend on the phone who said, "oh, it is much colder than that here it is 0 degrees fahrenheit here", explain how that can be true., there is no relationship between celsius and fahrenheit temperatures., 0 degrees celsius is colder than 0 degrees fahrenheit., 0 degrees celsius is equal to 32 degrees fahrenheit., 0 degrees fahrenheit is warmer than 0 degrees celsius., ron and landon are digging for the footer for a building. ron can do the job alone in 20 hours. landon can do the job alone in 30 hours. how long will it take both of them working together to do the job, videos related to solving multi-step problems.

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