# SAT Percentages Worksheet PDF with Answers | 1600.now Source: https://1600.now/sat-percentages-worksheet --- ## SAT Percentages Worksheet A percentage is measured relative to a base. For a percent change, use the original value as that base. For successive changes, multiply their factors rather than adding or subtracting the stated percentages. Written by [Luke Finigan](https://1600.now/about) The 12 questions cover discounts, reverse percentages, comparisons, and percentage points. Download the student worksheet or the explained answer-key version in Letter or A4. 12 questions · about 25 minutes · Problem-Solving and Data Analysis › Percentages [Download 4-page PDF](https://1600.now/downloads/worksheets/sat-percentages-worksheet-student-letter.pdf) [Share to Google Classroom](https://classroom.google.com/share?url=https%3A%2F%2F1600.now%2Fsat-percentages-worksheet) · This worksheet is free to print and share under [CC BY-NC-ND 4.0](https://creativecommons.org/licenses/by-nc-nd/4.0/). Tutors may also use it in paid sessions. If you post it online, please link to this page instead of re-uploading the PDF. These are original questions, not College Board items. ### Write the base and multiplier first For a change of $p\%$, the new amount is the original times $1+\dfrac p{100}$ for an increase or $1-\dfrac p{100}$ for a decrease. A 25% discount leaves 75% of the price; the discount itself is a different amount. For a reverse percentage, divide by the multiplier. If a fee after a 20% increase is 72 dollars, $1.20P=72$, so the original fee is 60 dollars. Subtracting 20% of 72 uses the wrong base. Apply successive multipliers to the changing amount. A 10% increase followed by a 10% decrease gives $1.10\cdot0.90=0.99$, or 99% of the original. A change from 40% to 50% is ten percentage points, but a 25% increase relative to 40%. Try it yourself: A value rises from 80 to 100. What is the percent increase? · A 20% B 25% C 80% ### Questions 1. **Question 1** A jacket originally costs $80 and is discounted by 25%. What is the sale price? A. $65 B. $20 C. $100 D. $60 **D.** The remaining price is 75% of $80: $0.75(80)=\$60$. The $20 discount is not the sale price. 2. **Question 2** After a 20% increase, a town's annual fee is $72. What was the fee before the increase? A. $57.60 B. $60 C. $52 D. $86.40 **B.** Let the original fee be $p$. Then $1.20p = 72$, so $p = 60$. Subtracting 20% of the new fee uses the wrong base. 3. **Question 3** A value increases by 10% and then decreases by 10%. The final value is what percent of the original? A. 99% B. 90% C. 100% D. 101% **A.** Multiply the change factors: $1.10(0.90)=0.99$. The result is 99% of the original, a net 1% decrease. 4. **Question 4** Positive quantity A is 150% of positive quantity B. Quantity B is what percent of quantity A? A. 150% B. 75% C. $66\dfrac{2}{3}\%$ D. 50% **C.** $\mathrm{A}=1.5\mathrm{B}$, so $\dfrac{\mathrm{B}}{\mathrm{A}}=\dfrac{1}{1.5}=\dfrac{2}{3}$. Multiplying by 100% gives $66\dfrac{2}{3}\%$. 5. **Question 5** A store's revenue rises from $240,000 to $300,000. What is the percent increase? A. 20% B. 25% C. 60% D. 125% **B.** The increase is $60,000. Divide by the original $240,000: $\dfrac{60000}{240000}=0.25$, or 25%. 6. **Question 6** A solution has a total mass of 200 grams, of which 15% is salt. If 100 grams of water is added and no salt is lost, what percent of the new solution's mass is salt? A. 15% B. 5% C. 7.5% D. 10% **D.** The salt mass stays $0.15(200)=30$ grams. Total mass becomes 300 grams, so the salt fraction is $\dfrac{30}{300}=10\%$. 7. **Question 7** A price is reduced by 30% to $84. What was the original price? A. $109.20 B. $114 C. $120 D. $126 **C.** After a 30% reduction, 70% of the original price remains. Thus $0.70p=84$, so $p=120$. 8. **Question 8** A school has 800 students, of whom 35% ride the bus. How many students do not ride the bus? A. 280 B. 365 C. 520 D. 765 **C.** The percentage not riding the bus is $100\%-35\%=65\%$. Multiplying 0.65 by 800 gives 520 students. 9. **Question 9** A population increases from 500 to 650. What is the percent increase? A. 23% B. 26% C. 30% D. 130% **C.** The increase is 150, measured against the original 500. Therefore $\dfrac{150}{500}=0.30$, or 30%. 10. **Question 10** The price of an item rises by 25%. By what percent must the new price decrease to return to the original price? A. 20% B. 25% C. 30% D. 75% **A.** If the original price is 100, the new price is 125. A decrease of 25 from 125 is $\dfrac{25}{125}=20\%$. 11. **Question 11** A survey reports that support rose from 40% to 50%. What is the relative percent increase in support? A. 10% B. 20% C. 25% D. 50% **C.** The increase is 10 percentage points. Relative to the original 40%, this is $\dfrac{10}{40}=25\%$; percentage points and percent change differ. 12. **Question 12** A worker earns $18 per hour and receives a 5% raise. What is the new hourly wage? A. $18.05 B. $18.50 C. $18.90 D. $19.80 **C.** Multiply the original wage by 1.05: $18(1.05)=18.90$. The increase is $0.90 per hour. 0/12 correct ### Check your percentages answers Each row is a wrong answer choice from one of the sheet's problems. Find the one you picked, then run the check in the last column. | What your answer looked like | What actually happened | Fix it next time | | --- | --- | --- | | $20 in problem 1 or 280 in problem 8 | You found the part that changes: the $20 discount, or the 280 students who ride the bus. Each question asks for what's left. | Use the remaining percent directly: 75% of $80 is $60, and 65% of 800 is 520. | | $57.60 in problem 2 or $109.20 in problem 7 | You took the percent of the new price. The 20% increase in problem 2 was 20% of the old fee, which you don't know yet. | Write the new price as a multiple of the original: $1.20p = 72$, so $p = 60$. In problem 7, $0.70p = 84$ gives $p = 120$. Check: 20% of 60 is 12, and $60 + 12 = 72$. | | 100% in problem 3 | A 10% increase and a 10% decrease don't cancel, because the decrease is 10% of a larger number. | Start with 100. Up 10% is 110, and 10% of 110 is 11, so down 10% leaves 99. That's 99% of the original, which matches $1.10 \times 0.90 = 0.99$. | | 20% in problem 5 or 23% in problem 9 | You divided the change by the new value: $\dfrac{60{,}000}{300{,}000} = 20\%$ and $\dfrac{150}{650} \approx 23\%$. | Divide by the starting value: $\dfrac{60{,}000}{240{,}000} = 25\%$ and $\dfrac{150}{500} = 30\%$. | | 25% in problem 10 | The decrease is measured from the new, higher price. A 25% drop from 125 lands at 93.75, not 100. | With an original price of 100, the new price is 125. Getting back to 100 means dropping 25 from 125: $\dfrac{25}{125} = 20\%$. | | 10% in problem 11 | 10 is the change in percentage points, $50 - 40$. The question asks for the relative increase. | Divide the change by the starting percent: $\dfrac{10}{40} = 25\%$. | #### Worked example: reversing a percent comparison Problem 4 says $A$ is 150% of $B$ and asks what percent $B$ is of $A$. Pick a number for $B$ to make it concrete. If $B = 100$, then $A = 150$. Now divide the part by the whole: $\dfrac{B}{A} = \dfrac{100}{150} = \dfrac{2}{3}$, or $66\tfrac{2}{3}\%$. The choice 50% assumes that since $A$ is 50% more than $B$, $B$ must be 50% less than $A$. But 50% less than 150 is 75, not 100. The choice 150% answers the question the other way around: $A$ as a percent of $B$. ### Apply the check to fresh questions For every percentage answer, write what 100% refers to before calculating. Continue with percentage practice and check reverse problems by applying the stated change to your result. [Practice percentages questions](https://1600.now/bank/math/skill/Percentages) [Review the percentages method](https://1600.now/sat-skill/percentages) ### More Math worksheets [All worksheets](https://1600.now/sat-worksheets) - [Ratios and Rates](https://1600.now/sat-ratios-rates-proportions-worksheet) - [Statistics](https://1600.now/sat-one-variable-data-worksheet) - [Two-Variable Data](https://1600.now/sat-two-variable-data-worksheet)