# Equations and Inequalities

## Objective

Solve word problems leading to equations in the forms ${px+q=r}$ and ${p(x+q)=r }$ (Part 2).

## Common Core Standards

### Core Standards

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#### References

EngageNY Mathematics Grade 7 Mathematics > Module 3 > Topic B > Lesson 8Example 1

Grade 7 Mathematics > Module 3 > Topic B > Lesson 8 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

### Problem 2

Your parents are redecorating the dining room and want to place two rectangular pictures, each measuring 25 inches across, on the wall, which measures ${10 {2\over3}}$ feet long. They want to place the pictures so that the distance between the pictures and the distances from each picture to the end of the wall are the same, as shown in the diagram below.

Determine the distance each picture should be placed from the ends of the wall. Explain the strategy that you used.

#### References

EngageNY Mathematics Grade 7 Mathematics > Module 3 > Topic B > Lesson 7Opening Exercise

Grade 7 Mathematics > Module 3 > Topic B > Lesson 7 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

### Problem 3

Three toothpick configurations are shown in the chart below.

1. Extend the pattern to complete the chart.
2. How many toothpicks will be in the 10th design?
3. Write an expression to represent the number of toothpicks in the $n$th design.
4. Which design will have 175 toothpicks? Write and solve an equation.

#### References

SERP Poster Problems Toothpick Patterns

Toothpick Patterns from Poster Problems is made available by SERP under the CC BY-NC-SA 4.0 license. Accessed Nov. 9, 2017, 12:50 p.m..

Modified by The Match Foundation, Inc.

## Problem Set

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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

• Include additional fluency practice of solving equations (without context).
• Challenge: Perla worked 4 hours at her job on Saturday and then spent $12.75 on her way home. She worked 5 hours on Sunday and earned 1.5 times her normal hourly rate because it was a holiday. She spent$8.50 on her way home on Sunday. If Perla had \$70.75 after her spending, determine her normal hourly rate.