Percent Problems in Context - ISEE Middle Level Quantitative Reasoning

1. A $40$-item quiz has $85\%$ correct. How many were correct?

   $34$. Multiply 40 by 0.85 to determine the number of correct answers.

2. A number is increased by $30\%$. What is the multiplier on the original?

   $1.30$. Add 1 to the decimal 0.30 to get the factor for a 30% increase.

3. A shirt costs $50 and is discounted $20\%$. What is the sale price?

   $40. Subtract 20% of $50 from the original price to get the discounted amount.

4. A price decreases from $90 to $72. What is the percent decrease?

   $20\%$. Divide the $18 decrease by the original $90 and multiply by 100.

5. Find the original amount if $8\%$ of it equals $12$.

   $150$. Divide 12 by 0.08 to solve for the whole amount.

6. What percent of $80$ is $12$?

   $15\%$. Divide 12 by 80 and multiply by 100 to express the ratio as a percentage.

7. What is $15\%$ of $60$?

   $9$. Convert 15% to 0.15 and multiply by 60 to find the part of the whole.

8. A $400 bill is split so one person pays $35\%$. How much do they pay?

   $140. Multiply $400 by 0.35 to find one person's share.

9. A population of $500$ grows by $12\%$. What is the new population?

   $560$. Multiply 500 by 1.12 to account for the 12% growth.

10. After a $10\%$ discount, a jacket costs $72. What was the original price?

    $80. Divide $72 by 0.9 to find the price before the 10% discount.

11. If $25\%$ of a number is $18$, what is the number?

    $72$. Divide 18 by 0.25 to solve for the whole when given 25% of it.

12. A price increases from $40 to $50. What is the percent increase?

    $25\%$. Divide the $10 increase by the original $40 and multiply by 100.

13. A bill is $80 before tip. What is a $15\%$ tip amount?

    $12. Multiply $80 by 0.15 to calculate the tip based on the bill.

14. A store sells $45$ of $60$ items. What percent of the items were sold?

    $75\%$. Divide 45 by 60 and multiply by 100 to get the percentage sold.

15. A test score improves from $70$ to $84$. What is the percent increase?

    $20\%$. Divide the 14-point increase by the original 70 and multiply by 100.

16. A class has $24$ students; $75\%$ are present. How many are present?

    $18$. Multiply 24 by 0.75 to find the number of present students.

17. A $6\%$ sales tax is added to $200. What is the total cost?

    $212. Add 6% of $200 to the original cost for the total including tax.

18. A $120 item is marked up $25\%$. What is the new price?

    $150. Multiply $120 by 1.25 to apply the 25% markup.

19. A number is decreased by $18\%$. What is the multiplier on the original?

    $0.82$. Subtract 0.18 from 1 to get the factor for an 18% decrease.

20. State the percent equation that relates part, whole, and percent $p$.

    $\text{part}=\frac{p}{100}\times\text{whole}$. This formula calculates the part by converting the percent to a decimal and multiplying by the whole.

21. State the formula for finding percent $p$ given part and whole.

    $p=\frac{\text{part}}{\text{whole}}\times 100$. This formula finds the percent by dividing the part by the whole and multiplying by 100.

22. State the formula for percent change from old to new value.

    $\frac{\text{new}-\text{old}}{\text{old}}\times 100\%$. This formula computes the percentage change relative to the original value.

23. Find and correct the error: $30\%$ of $50$ is computed as $0.30+50=50.30$.

    Correct: $0.30\times 50=15$. The error is adding instead of multiplying; percentage requires multiplication by the decimal.

24. A solution is $20\%$ salt by mass. In $250$ g, how many grams are salt?

    $50\text{ g}$. Multiply 250 g by 0.20 to calculate the mass of salt.

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