Ratios & Percent - GED Math

1. Apples cost 6 dollars for $4$ pounds. What is the unit price?

   1.50 dollars per pound. Divide the cost by the quantity: $6 \div 4 = 1.5$.

2. The ratio of boys to girls in a class of $40$ is $3 : 5$. How many boys are there?

   $15$. There are $3 + 5 = 8$ parts, each part is $5$ students, and $3 \times 5 = 15$.

3. What is the simple interest on 500 dollars at $4\%$ per year for $3$ years?

   60 dollars. $I = Prt = 500 \times 0.04 \times 3$.

4. In the simple interest formula $I = Prt$, what do $P$, $r$ and $t$ stand for?

   $P$ is the principal (starting amount), $r$ is the annual rate as a decimal, and $t$ is the time in years.

5. A price rises from 40 dollars to 50 dollars. What is the percent increase?

   $25\%$. The change is 10 dollars, and 10 divided by 40 is 0.25.

6. $18$ is what percent of $72$?

   $25\%$. $\frac{18}{72} = \frac{1}{4}$.

7. How do you solve a proportion $\frac{a}{b} = \frac{c}{d}$?

   Cross multiply: $ad = bc$, then solve for the unknown.

8. What is the formula for percent change?

   $\frac{\text{new} - \text{original}}{\text{original}} \times 100\%$. Always divide by the original amount.

9. An item that costs 60 dollars is marked $20\%$ off. What is the sale price?

   48 dollars. Paying $80\%$ of the price: $0.8 \times 60 = 48$.

10. On a map, $1$ inch represents $5$ miles. How many miles do $4.5$ inches represent?

    $22.5$ miles. $4.5 \times 5 = 22.5$.

11. What is $15\%$ of $80$?

    12. Convert the percent to a decimal and multiply: 0.15 times 80 is 12.

12. A price rises $10\%$ and then falls $10\%$. What percent of the original price is the final price?

    $99\%$. Multiply the factors: 1.1 times 0.9 is 0.99. The second change applies to a larger amount.

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