Training Percents Percent Word Problems
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Percent Word Problems

24 min Percents

Percent Word Problems

Percent word problems bring together everything you have learned about percents — conversions, basic calculations, and percent change — and challenge you to apply those skills in realistic scenarios.

Success with word problems depends on careful reading. You must identify what quantity represents the whole, what represents the part, and what the question is actually asking before you set up any equation.

This lesson presents a variety of percent word problems drawn from shopping, finance, statistics, and science to build your confidence and flexibility.

Translate carefully: identify the part, the whole, and the percent, then use the percent equation or proportion.

Example 1

A student answered 42 out of 60 questions correctly. What percent?

$$\frac{42}{60} = 0.70 = 70\%$$

Example 2

A laptop originally costs $\$850$. After a $15\%$ discount and $8\%$ sales tax on the sale price, what is the final cost?

  1. Discount: $0.15 \times 850 = \$127.50$
  2. Sale price: $850 - 127.50 = \$722.50$
  3. Tax: $0.08 \times 722.50 = \$57.80$
  4. Final: $722.50 + 57.80 = \$780.30$
Example 3

A town grew from $12{,}500$ to $14{,}000$. Percent increase?

$$\frac{14{,}000 - 12{,}500}{12{,}500} \times 100\% = \frac{1{,}500}{12{,}500} \times 100\% = 12\%$$

Example 4

After a $20\%$ raise, Maria earns $\$54{,}000$. Original salary?

$54{,}000 = 1.20 \times \text{Original}$

$$\text{Original} = \frac{54{,}000}{1.20} = \$45{,}000$$

Example 5

A store marks up goods $60\%$ over cost. If the selling price is $\$128$, what was the cost?

$128 = 1.60 \times \text{Cost}$. Cost $= \dfrac{128}{1.60} = \$80$.

Example 6

In a class of 40, $35\%$ are left-handed. How many are right-handed?

Left-handed: $0.35 \times 40 = 14$. Right-handed: $40 - 14 = 26$.

Practice Problems

1. A car was $\$24{,}000$ new and is now worth $\$15{,}600$. Percent decrease?
2. Sales tax is $7.5\%$. You pay $\$53.75$ total. Original price?
3. 180 of 450 employees are women. What percent?
4. After a $10\%$ discount and $6\%$ tax, a TV costs $\$572.40$. Original price?
5. A savings account earns $3.5\%$ simple interest. Balance after 4 years on $\$2{,}000$?
6. Your weight drops from 185 lbs to 170 lbs. Percent decrease (nearest tenth)?
7. A farmer plants corn on $120$ of $480$ acres. What percent?
8. After two successive $10\%$ discounts, what single percent discount is equivalent?
9. Invest $\$10{,}000$ at $6\%$ simple interest. When does the interest reach $\$3{,}000$?
10. A basketball player made 72 of 90 free throws. Percentage?
11. A $\$45$ meal with $18\%$ tip and $8\%$ tax (both on original). Total?
12. A house increased $12\%$ to $\$280{,}000$. Original value?
Show Answer Key

1. $35\%$

2. $\$50$

3. $40\%$

4. $\$600$ (sale $= 0.90x$, total $= 0.90x \times 1.06 = 0.954x = 572.40$)

5. $I = 2000 \times 0.035 \times 4 = \$280$; balance = $\$2{,}280$

6. $\dfrac{15}{185} \approx 8.1\%$

7. $25\%$

8. $19\%$ (since $0.90 \times 0.90 = 0.81 = 81\%$ of original)

9. $t = \dfrac{3000}{10000 \times 0.06} = 5$ years

10. $80\%$

11. $45 + 8.10 + 3.60 = \$56.70$

12. $\dfrac{280000}{1.12} = \$250{,}000$

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