Percent Applications: practice solutions, Grade 7 – download the PDF

1 Percent of a number ★★★

\( 25\% = 0.25 \), so \( 0.25 \times 180 = 45 \).

Answer: 45 students.

2 Percents and decimals ★★★

a) \( 7\% = \dfrac{7}{100} = 0.07 \).

b) \( 0.4 = 0.40 = 40\% \).

c) \( 3 \div 8 = 0.375 = 37.5\% \).

d) \( 0.12 \times 50 = 6 \).

3 Up 10%, down 10% ★★★

10% of 60 is 6 pounds.

Increase: \( 60 + 6 = 66 \) pounds. Decrease: \( 60 - 6 = 54 \) pounds.

4 Sneaker sale ★★★

Discount: \( 0.25 \times 80 = 20 \) dollars.

Sale price: \( 80 - 20 = 60 \) dollars.

Answer: The sneakers cost $60 on sale.

5 Book with tax ★★★

Tax: \( 0.08 \times 25 = 2.00 \) dollars.

Total: \( 25 + 2 = 27 \) dollars.

Answer: $27.00.

6 Tipping at dinner ★★★

10% of 40 is 4. So 20% is \( 2 \times 4 = 8 \) dollars, and 15% is \( 4 + 2 = 6 \) dollars.

Check: \( 0.15 \times 40 = 6 \). Answer: $6 and $8.

7 A small savings account ★★★

\( I = Prt = 500 \times 0.03 \times 2 = 30 \) dollars.

Balance: \( 500 + 30 = 530 \) dollars.

Answer: $30 of interest, $530 in all.

8 Find the percent increase ★★★

Change: \( 52 - 40 = 12 \).

\( \dfrac{12}{40} = 0.30 = 30\% \).

Answer: a 30% increase.

9 Find the percent decrease ★★★

Change: \( 250 - 200 = 50 \).

\( \dfrac{50}{250} = 0.20 = 20\% \).

Answer: a 20% decrease (divide by the original price, 250).

10 Store markup ★★★

Markup: \( 0.45 \times 36 = 16.20 \) dollars.

Selling price: \( 36 + 16.20 = 52.20 \) dollars.

Answer: $52.20.

11 Tax on a purchase ★★★

Tax: \( 0.065 \times 120 = 7.80 \) dollars.

Total: \( 120 + 7.80 = 127.80 \) dollars.

Shortcut: \( 1.065 \times 120 = 127.80 \).

12 Salesperson pay ★★★

Commission: \( 0.08 \times 9500 = 760 \) dollars.

Total pay: \( 400 + 760 = 1160 \) dollars.

Answer: $1,160.

13 Measuring a ruler ★★★

Error: \( |9.6 - 10| = 0.4 \).

\( \dfrac{0.4}{10} = 0.04 = 4\% \).

Answer: the percent error is 4%.

14 Monthly sales chart ★★★

Jan to Feb: \( \dfrac{50 - 40}{40} = 0.25 \), a 25% increase.

Feb to Mar: \( \dfrac{50 - 45}{50} = 0.10 \), a 10% decrease.

Mar to Apr: \( \dfrac{54 - 45}{45} = 0.20 \), a 20% increase.

Each time we divide by the earlier month’s value.

15 Find the original price ★★★

The sale price is 70% of the original: \( 0.70 \times p = 42 \).

\( p = 42 \div 0.70 = 60 \).

Check: 30% of 60 is 18, and \( 60 - 18 = 42 \). Answer: $60.

16 Up 20%, then down 20% ★★★

Up 20%: \( 50 \times 1.20 = 60 \).

Down 20% of 60: \( 60 \times 0.80 = 48 \).

The final price is $48, not $50. Net change: \( \dfrac{48 - 50}{50} = -0.04 \), a 4% decrease. The 20% decrease is taken from a larger number, so it removes more.

17 How long was the deposit? ★★★

\( I = Prt \), so \( 360 = 2000 \times 0.045 \times t = 90t \).

\( t = 360 \div 90 = 4 \).

Answer: 4 years.

18 Find the interest rate ★★★

\( 216 = 1200 \times r \times 3 = 3600r \).

\( r = 216 \div 3600 = 0.06 \).

Answer: 6% per year.

19 Restaurant total ★★★

Tax: \( 0.08 \times 55 = 4.40 \). Tip: \( 0.18 \times 55 = 9.90 \).

Total: \( 55 + 4.40 + 9.90 = 69.30 \) dollars.

Answer: $69.30.

20 Two-tier commission ★★★

First part: \( 0.05 \times 4000 = 200 \) dollars.

Sales above 4,000: \( 7500 - 4000 = 3500 \). Commission: \( 0.08 \times 3500 = 280 \) dollars.

Total: \( 200 + 280 = 480 \) dollars. Answer: $480.

21 Which scale is better? ★★★

Scale A: \( \dfrac{|148 - 160|}{160} = \dfrac{12}{160} = 0.075 = 7.5\% \).

Scale B: \( \dfrac{|157 - 160|}{160} = \dfrac{3}{160} = 0.01875 \approx 1.9\% \).

Answer: scale B is more accurate, because its percent error is smaller.

22 Card fee ★★★

Percent fee: \( 0.029 \times 50 = 1.45 \). Flat fee: 0.30.

Total fee: \( 1.45 + 0.30 = 1.75 \) dollars.

Store keeps: \( 50 - 1.75 = 48.25 \) dollars. Answer: $48.25.