Lesson 12

Solving Problems about Percent Increase or Decrease

Let’s use tape diagrams, equations, and reasoning to solve problems with negatives and percents.

Problem 1

A backpack normally costs $25 but it is on sale for $21. What percentage is the discount?

(From Unit 4, Lesson 12.)

Problem 2

Find each product.

  1. \(\frac25 \boldcdot (\text-10)\)
  2. \(\text-8 \boldcdot \left(\frac {\text{-}3}{2}\right)\)
  3. \(\frac{10}{6} \boldcdot 0.6\)
  4. \(\left(\frac {\text{-}100}{37}\right) \boldcdot (\text-0.37)\)
(From Unit 5, Lesson 9.)

Problem 3

Select all expressions that show \(x\) increased by 35%.






\(x + \frac{35}{100}x\)


\(( 1+0.35)x\)




\((100 + 35)x\)

Problem 4

Complete each sentence with the word discount, deposit, or withdrawal.

  1. Clare took $20 out of her bank account. She made a _____.
  2. Kiran used a coupon when he bought a pair of shoes. He got a _____.
  3. Priya put $20 into her bank account. She made a _____.
  4. Lin paid less than usual for a pack of gum because it was on sale. She got a _____.
(From Unit 4, Lesson 11.)

Problem 5

Here are two stories:

  • The initial freshman class at a college is 10% smaller than last year’s class. But then during the first week of classes, 20 more students enroll. There are then 830 students in the freshman class.
  • A store reduces the price of a computer by $20. Then during a 10% off sale, a customer pays $830.

Here are two equations:

  • \(0.9x+20=830\)
  • \(0.9(x-20)=830\)
  1. Decide which equation represents each story.
  2. Explain why one equation has parentheses and the other doesn’t.
  3. Solve each equation, and explain what the solution means in the situation.