# 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%.

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.

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.