Multi-Step Word Problems — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
Lily bought a jacket for $78 and a hat for $23. She paid with $120. Her change is $29 because 78 + 23 = 101 and 120 − 101 = 29.
Corrected: Lily bought a jacket for $78 and a hat for $23. She paid with $120. Her change is $19 because 78 + 23 = 101 and 120 − 101 = 19.
The addition is right (78 + 23 = 101), but the subtraction was off. 120 − 101 = 19, not 29, so Lily's change is $19.
2. Fix the sentence:
A rope is 450 cm long. A worker cuts off 168 cm and then 195 cm. There are 97 cm left because 450 − 168 = 282 and 282 − 195 = 97.
Corrected: A rope is 450 cm long. A worker cuts off 168 cm and then 195 cm. There are 87 cm left because 450 − 168 = 282 and 282 − 195 = 87.
After the first cut, 450 − 168 = 282 cm remain. Then 282 − 195 = 87, not 97, so 87 cm of rope are left.
3. Fix the sentence:
A store earned $935 on Saturday and $748 on Sunday. After paying $580 in expenses, the profit is $1,113 because 935 + 748 = 1,693 and 1,693 − 580 = 1,113.
Corrected: A store earned $935 on Saturday and $748 on Sunday. After paying $580 in expenses, the profit is $1,103 because 935 + 748 = 1,683 and 1,683 − 580 = 1,103.
The original sentence added 935 + 748 incorrectly. The true sum is 1,683, and 1,683 − 580 = 1,103, so the store's profit is $1,103.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. A plumber has 750 cm of pipe. He uses 284 cm on one job and 195 cm on another. He has 271 cm left.
Add the two amounts used first: 284 + 195 = 479 cm. Then subtract from the starting length: 750 − 479 = 271 cm of pipe left.
2. Maya saved $465 in January and $390 in February. She spent $275 on art supplies. She has $580 remaining.
Maya's two months of saving total 465 + 390 = $855. After spending $275 on art supplies, 855 − 275 = $580 remains.
3. A container holds 2,000 mL of juice. After pouring out 875 mL in the morning and 640 mL at lunch, there are 485 mL left.
Pour out both servings: 875 + 640 = 1,515 mL gone. Subtract from the full container: 2,000 − 1,515 = 485 mL still in it.
4. Ben earned $340 mowing lawns and $215 washing cars. He bought a game for $129. He has $426 left.
Ben's earnings combine to 340 + 215 = $555. Buying a $129 game leaves 555 − 129 = $426.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. A garden bed is 960 cm long. A gardener plants flowers along 385 cm and vegetables along 290 cm. How many centimeters are unused? Show your steps.
Sample answer: Step 1: 385 + 290 = 675 cm are used. Step 2: 960 − 675 = 285 cm are unused.
First find the total length used by adding 385 + 290 = 675 cm, since both the flowers and vegetables share the same 960 cm bed. Then subtract that combined length from the whole bed: 960 − 675 = 285 cm, which is the unused portion.
2. Why is it important to check whether your answer makes sense after solving a multi-step problem?
Sample answer: Checking your answer helps you catch mistakes like using the wrong operation or making an arithmetic error. If the answer seems too large or too small for the situation, you know to go back and fix a step.
Multi-step problems give many chances to slip up, like adding when you should subtract or miscarrying a digit, so a quick check protects against those errors. Comparing the answer to the situation, such as noticing that change cannot be larger than the amount paid, signals when a step needs to be redone.