# 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?

### Problem 2

Find each product.

- \(\frac25 \boldcdot (\text-10)\)
- \(\text-8 \boldcdot \left(\frac {\text{-}3}{2}\right)\)
- \(\frac{10}{6} \boldcdot 0.6\)
- \(\left(\frac {\text{-}100}{37}\right) \boldcdot (\text-0.37)\)

### Problem 3

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

A:

\(1.35x\)

B:

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

C:

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

D:

\(( 1+0.35)x\)

E:

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

F:

\((100 + 35)x\)

### Problem 4

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

- Clare took $20 out of her bank account. She made a _____.
- Kiran used a coupon when he bought a pair of shoes. He got a _____.
- Priya put $20 into her bank account. She made a _____.
- Lin paid less than usual for a pack of gum because it was on sale. She got a _____.

### 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:

- \(0.9x+20=830\)
- \(0.9(x-20)=830\)

- Decide which equation represents each story.
- Explain why one equation has parentheses and the other doesn’t.
- Solve each equation, and explain what the solution means in the situation.