Lesson 12
Solving Problems about Percent Increase or Decrease
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.