Percent Increase/Decrease - Pre Algebra

1. A jacket priced at 60 dollars is discounted $20\%$. What is the sale price?

   48 dollars. Multiply by $0.8$: $60 \times 0.8 = 48$.

2. What single multiplier applies a $30\%$ decrease to a quantity?

   $0.70$. After a $30\%$ decrease, $70\%$ of the original remains.

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

   $25\%$. The change is 10, and $\frac{10}{40} = 0.25$.

4. A quantity doubles. What is the percent increase?

   $100\%$. The increase equals the original amount, so the change is $\frac{x}{x} = 1 = 100\%$.

5. A town's population falls from 800 to 600. What is the percent decrease?

   $25\%$. The decrease is 200, and $\frac{200}{800} = 0.25$.

6. A price is increased by $10\%$ and the new price is then decreased by $10\%$. What is the overall percent change?

   A $1\%$ decrease. The multipliers combine: $1.1 \times 0.9 = 0.99$, which is $99\%$ of the original.

7. What single multiplier applies a $15\%$ increase to a quantity?

   $1.15$. The new amount is the original $100\%$ plus $15\%$, which is $115\%$.

8. A price rises from 40 dollars to 50 dollars and later drops back to 40 dollars. What is the percent decrease for the drop?

   $20\%$. The drop of 10 is compared to 50, the value before the drop: $\frac{10}{50} = 0.2$.

9. What is 80 increased by $25\%$?

   $100$. Multiply by $1.25$: $80 \times 1.25 = 100$.

10. After a $25\%$ increase, a price is 100 dollars. What was the original price?

    80 dollars. Divide by the multiplier: $100 \div 1.25 = 80$.

11. When computing a percent change, which value goes in the denominator?

    The original (starting) value. The change is always compared to where the quantity began, not to the new value.

12. What is the formula for percent change?

    $\frac{\text{new} - \text{original}}{\text{original}} \times 100\%$. A positive result is an increase and a negative result is a decrease.

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