Multi-step percent problems drills

Solve multi-step percent word problems combining several percent ideas.

Free, timed SHSAT practice sets on multi-step percent problems— every question includes a full worked explanation, and there's no account required.

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How to solve multi-step percent word problems

Multi-step percent problems chain two or three simple percent steps. The key is to know which number each percent is taken of.

  1. List the steps in the order the story gives them.
  2. Turn each step into a multiplier (20% off is \(\times 0.80\); 8% tax is \(\times 1.08\)) or a division (if 35% of the whole is 140, the whole is \(140 \div 0.35 = 400\)).
  3. Apply each step to the result of the step before it.

Example: a 50-dollar item is 20% off, and then 8% tax is added to the sale price: \(50 \times 0.80 \times 1.08 = 43.20\) dollars.

Traps:

Worked examples

Example 1.
A tablet regularly costs \(\$205.00\). It is on sale for 4% off, and then 8% sales tax is applied to the discounted price. What is the total cost?
Show answer and explanation
Answer:
C

Sale price \(= \$205.00 \times (1 - 4/100) = \$196.80\); tax \(= \$196.80 \times 8/100 = \$15.744 \approx \$15.74\); total \(= \$212.54\). (Figuring the tax on the original price (8% of \(\$205.00\) is $16.40) gives $213.20. Forgetting to add the tax gives $196.80. Subtracting the tax instead of adding it gives about $181.06.)

Example 2.
At the company, 64% of all employees signed up for art club, which comes to 144 employees. Separately, 28% of ALL the employees signed up for chess club. How many employees signed up for chess club?
Show answer and explanation
Answer:
A

From step 1: 64% of the whole is 144, so the whole is \(144 \times 100 \div 64 = 225\) employees. Then 28% of 225 \(= 63\) employees signed up for chess club. (Stopping at the total number of employees gives 225. Finding the total with 36% instead of 64% (\(144 \times 100 \div 36\)) and then taking 28% of it gives 112. Finding the employees who did NOT sign up for chess club (\(225 - 63\)) gives 162.)

Example 3.
The population of a town was 6480. It grew by 10% one year, then declined by 25% the next year. What is the population after both years?
Show answer and explanation
Answer:
D

After growth: 6480 \(\times (1 + 10/100) = 7128\). After decline: 7128 \(\times (1 - 25/100) = 5346\). (Combining +10% and -25% into one 15% decrease of 6480 gives 5508. Stopping after the first year gives 7128. Reporting only the change in population (\(6480 - 5346\)) gives 1134.)