Word problems: turn the sentence into a plan.
Read for the quantity you need, not a keyword that seems to suggest an operation. A short plan prevents a long calculation in the wrong direction.
Reviewed · Official ASVAB scope and calculator guidance. Examples are original AptiStep material.
Write what the question asks
Before using any number, finish this sentence: “I need to find ___, measured in ___.” A question may give a distance and a time but ask for another distance, a speed, or an arrival time. Those are different problems even when the same numbers appear.
Keep units beside the numbers
If a cyclist travels 24 miles in 2 hours, the rate is 12 miles per hour. Multiplying by 3 hours cancels the hour unit and gives 36 miles. Dividing 12 by 3 would produce the wrong relationship for distance traveled over more time.
Be careful with “more” and “less”
“Sam has 4 more tickets than Lee. Sam has 11. How many does Lee have?” contains the word more, but the answer is 11 − 4 = 7. Draw a small relationship or rewrite the sentence: Lee’s tickets + 4 = 11. Let the relationship choose the operation.
Try a proportional recipe
A mix uses 2 cups of concentrate for every 5 cups of water. How much concentrate goes with 15 cups of water?
Show the solution
The water amount is multiplied by 3, so the concentrate is also multiplied by 3: 2 × 3 = 6 cups. Keep the ratio concentrate:water in the same order.
Use a three-line scratch-work habit
Write the target with its unit, the relationship, and the calculation. Afterward, check whether the answer changes in the direction you expect. Save speed practice for after you can reliably set up the problem.
Four fresh questions
Try each example before opening its answer. Then explain the step you used in your own words.
Five identical boxes weigh 35 pounds in total. What do eight boxes weigh?
Show answer and reasoning
56 pounds
Find one box: 35 ÷ 5 = 7 pounds. Scale to eight: 7 × 8 = 56 pounds. Keep the weight per box constant.
A van travels 150 miles in 3 hours at a steady speed. How long would 250 miles take at that speed?
Show answer and reasoning
5 hours
The speed is 150 ÷ 3 = 50 miles per hour. Required time is distance divided by speed: 250 ÷ 50 = 5 hours. The question asks for time, not another distance.
A shelf has 24 books. One quarter are reference books. How many are not reference books?
Show answer and reasoning
18 books
One quarter of 24 is 6. The requested group is the remaining books, so subtract: 24 − 6 = 18. Stopping after the first calculation answers a different question.
A worker earns $16 per hour for 7 hours and spends $12 on transport. How much remains from that pay?
Show answer and reasoning
$100
First find gross pay for this example: 16 × 7 = 112 dollars. Then subtract the stated transport cost: 112 − 12 = 100. No other deductions are specified.
Can you explain the method without looking?
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