Percent and percent change

Advanced Math 6 · Unit 7 · percent-change · Teacher edition

percent-change

Name ______________________________Date ______________

1.
Increase $80$ by $25\%$ .
Answer: ______________
2.
$15\%$ of what number is $36$ ?
Answer: ______________
3.
A price rose from $40 to $50. What was the percent increase?
Answer: ______________
4.
A jacket costs $45 after a $25\%$ discount. What was the original price?
1. (A)
  $33.75
2. (B)
  $56.25
3. (C)
  $60
4. (D)
  $70
5.
A number is decreased by $20\%$ , and the result is then increased by $20\%$ . The final value is what percent of the original? Enter the percent as a number.
Answer: ______________

Answer key — Percent and percent change

1.
100percent-change-01
$25\%$ of $80$ is $20$ ; $80 + 20 = \mathbf{100}$ . Or in one step: $80 \times 1.25 = 100$ .
2.
240percent-change-02
One percent is $36 \div 15 = 2.4$ , so $100\%$ is $2.4 \times 100 = \mathbf{240}$ . Check: $0.15 \times 240 = 36$ . ✓
3.
25percent-change-03
$\frac{10}{40} = \frac{1}{4} = \mathbf{25}\%$ . (Measuring against the new price, $\frac{10}{50} = 20\%$ , is the wrong base.)
4.
(C)
$60
percent-change-04
$45 is three quarters of the original, so one quarter is $15 and the original is $4 \times 15 = \mathbf{60}$ . ($56.25 adds $25\%$ of $45$ — the wrong base. $33.75 discounts again.)
5.
96percent-change-05
Start at $100$ : $\to 80 \to 96$ . The final value is $\mathbf{96}\%$ of the original — a net $4\%$ loss, because the increase was $20\%$ of the smaller number. In one line: $0.8 \times 1.2 = 0.96$ .