Question

solve the word problem using the percent proportion or percent equation. make sure you show either the proportion or equation before solving. sometimes you will have to do extra steps at the end to solve the problem. follow rounding directions. 1) a woman put a total of $580 into a savings account for one year. the rate of interest on the account was 6½%. how much was the interest for the year in dollars and cents? (round to the nearest cent) 2) a student answered 86 problems on a test correctly and received a grade of 98%. how many problems were on the test, if all the problems were worth the same number of points? (round to the nearest whole number) 3) manuel found a wrecked trans - am that he could fix. he bought the car for 65% of the original price of $7200. what did he pay for the car? (round to nearest dollar) 4) a crew is made up of 9 men; the rest are women. 75% of the crew are men. how many people are in the crew? 5) ben earns $12,800 a year. about 15% is taken out for taxes. how much is taken out for taxes? 6) at a sale, shirts were sold for $15 each. this price was 80% of their original price. what was the original price? 7) there are 32 students in a class. nine of those students are women. what percent are men? (round to the nearest tenth) 8) the royals softball team played 75 games and won 55 of them. what percent of the games did they lose? (round to the nearest tenth)

Explanation:

Step1: Define simple interest formula

Simple interest: $I = P \times r \times t$
$P = 580$, $r = 0.065$, $t = 1$

Step2: Calculate interest

$I = 580 \times 0.065 \times 1 = 37.70$

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Step1: Set up percent proportion

$\frac{86}{x} = \frac{98}{100}$

Step2: Solve for total problems

$98x = 86 \times 100$
$x = \frac{8600}{98} \approx 87.76 \approx 88$

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Step1: Calculate 65% of original price

$Cost = 7200 \times 0.65$

Step2: Compute final cost

$Cost = 4680$

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Step1: Set up percent equation

$0.75x = 9$

Step2: Solve for total crew size

$x = \frac{9}{0.75} = 12$

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Step1: Calculate 15% of annual income

$Taxes = 12800 \times 0.15$

Step2: Compute tax amount

$Taxes = 1920$

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Step1: Set up percent equation

$0.80x = 15$

Step2: Solve for original price

$x = \frac{15}{0.80} = 18.75$

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Step1: Find number of male students

$Male = 32 - 9 = 23$

Step2: Calculate percent of men

$\% Male = \frac{23}{32} \times 100 \approx 71.9\%$

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Step1: Find number of lost games

$Lost = 75 - 55 = 20$

Step2: Calculate loss percentage

$\% Lost = \frac{20}{75} \times 100 \approx 26.7\%$

Answer:

1. $\$37.70$
2. 88 problems
3. $\$4680$
4. 12 people
5. $\$1920$
6. $\$18.75$
7. $71.9\%$
8. $26.7\%$