# Problem Solving when the Percent Changes

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Lesson Plans and Worksheets for Grade 7
Lesson Plans and Worksheets for all Grades

Examples, videos, and solutions to help Grade 7 students learn how to identify the original price as the whole and use their knowledge of percent and proportional relationships to solve multistep markup and markdown problems.

### Lesson 9 Student Outcomes

• Students solve percent problems where quantities and percents change.
• Students use a variety of methods to solve problems where quantities and percents change, including double number lines, visual models, and equations.

Lesson 9 Classwork

Example 1
Tom’s money is 75% of Sally’s money. After Sally spent \$120 and Tom saved all his money, Tom’s money is 50% more than Sally’s. How much money did each have at the beginning? Use a visual model and a percent line to solve the problem.

Example 2
Erin and Sasha went to a candy shop. Sasha bought 50% more candies than Erin. After Erin bought 8 more candies, Sasha had 20% more. How many candies did Erin and Sasha have at first?
a. Model the situation using a visual model.
b. How many candies did Erin have at first? Explain.

Example 3
Kimberly and Mike have an equal amount of money. After Kimberly spent \$50 and Mike spent \$25, Mike’s money is 50% more than Kimberly’s. How much did Kimberly and Mike have at first?
a. Use an equation to solve the problem.
b. Use a visual model to solve the problem.
c. Which method do you prefer and why?

Exercise
Todd has 250% more video games than Jaylon. Todd has 56 video games in his collection. He gives Jaylon 8 of his games. How many video games did Todd and Jaylon have in the beginning? How many do they have now?

Exercises 1–3
Calculate the percent error for Problems 1–3. Leave your final answer in fraction form, if necessary.
1. A realtor expected 18 people to show up for an open house, 25 but attended.
2. In science class, Mrs. Moore’s students were directed to weigh a 300 gram mass on the balance scale. Tina weighed the object and reported 328 grams.
3. Darwin’s coach recorded that he had bowled 250 points out of 300 in a bowling tournament. However, the official scoreboard showed that Darwin actually bowled points 225 out of 300.

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