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Home / Practice / Maths
Undoing operations in reverse order, and turning a word problem into an equation first.
Question 1 of 12
Charlie buys some bags of marbles. Each bag holds 10 marbles, and Charlie already had 13 marbles at home. That makes 83 marbles altogether. How many bags did Charlie buy?
Let n be the number of bags. Each bag holds 10, so the bags give 10n, and the 13 already at home are added on: 10n + 13 = 83. Take the 13 off both sides: 10n = 83 − 13 = 70. Then divide by 10: n = 70 ÷ 10 = 7. Dividing 83 by 10 straight away gives 8 and quietly counts the 13 already at home as though they came in bags. Look for the amount that is there whatever happens — it gets added on, not multiplied.
The answer is B. Let n be the number of bags. Each bag holds 10, so the bags give 10n, and the 13 already at home are added on: 10n + 13 = 83. Take the 13 off both sides: 10n = 83 − 13 = 70. Then divide by 10: n = 70 ÷ 10 = 7. Dividing 83 by 10 straight away gives 8 and quietly counts the 13 already at home as though they came in bags. Look for the amount that is there whatever happens — it gets added on, not multiplied.
Arjun buys some packs of stickers. Each pack holds 10 stickers, and Arjun already had 10 stickers at home. That makes 50 stickers altogether. How many packs did Arjun buy?
Let n be the number of packs. Each pack holds 10, so the packs give 10n, and the 10 already at home are added on: 10n + 10 = 50. Take the 10 off both sides: 10n = 50 − 10 = 40. Then divide by 10: n = 40 ÷ 10 = 4. Dividing 50 by 10 straight away gives 5 and quietly counts the 10 already at home as though they came in packs. Look for the amount that is there whatever happens — it gets added on, not multiplied.
The answer is B. Let n be the number of packs. Each pack holds 10, so the packs give 10n, and the 10 already at home are added on: 10n + 10 = 50. Take the 10 off both sides: 10n = 50 − 10 = 40. Then divide by 10: n = 40 ÷ 10 = 4. Dividing 50 by 10 straight away gives 5 and quietly counts the 10 already at home as though they came in packs. Look for the amount that is there whatever happens — it gets added on, not multiplied.
Solve 2x + 15 = 37.
Undo the operations in reverse order. The 15 was added last, so subtract it first: 37 − 15 = 22, so 2x = 22. Then undo the multiplication: 22 ÷ 2 = 11, so x = 11. Whatever is done to one side must be done to the other — that is the only rule in the topic. Checking: 2 × 11 + 15 = 37, which matches. Always substitute your answer back into the original. An equation checks itself in seconds.
The answer is A. Undo the operations in reverse order. The 15 was added last, so subtract it first: 37 − 15 = 22, so 2x = 22. Then undo the multiplication: 22 ÷ 2 = 11, so x = 11. Whatever is done to one side must be done to the other — that is the only rule in the topic. Checking: 2 × 11 + 15 = 37, which matches. Always substitute your answer back into the original. An equation checks itself in seconds.
Freya buys some packs of stickers. Each pack holds 6 stickers, and Freya already had 18 stickers at home. That makes 84 stickers altogether. How many packs did Freya buy?
Let n be the number of packs. Each pack holds 6, so the packs give 6n, and the 18 already at home are added on: 6n + 18 = 84. Take the 18 off both sides: 6n = 84 − 18 = 66. Then divide by 6: n = 66 ÷ 6 = 11. Dividing 84 by 6 straight away gives 14 and quietly counts the 18 already at home as though they came in packs. Read your answer back into the story to check it makes sense.
The answer is D. Let n be the number of packs. Each pack holds 6, so the packs give 6n, and the 18 already at home are added on: 6n + 18 = 84. Take the 18 off both sides: 6n = 84 − 18 = 66. Then divide by 6: n = 66 ÷ 6 = 11. Dividing 84 by 6 straight away gives 14 and quietly counts the 18 already at home as though they came in packs. Read your answer back into the story to check it makes sense.
Solve 5x − 3 = 62.
Undo the operations in reverse order. The 3 was taken away last, so add it first: 62 + 3 = 65, so 5x = 65. Then undo the multiplication: 65 ÷ 5 = 13, so x = 13. Whatever is done to one side must be done to the other — that is the only rule in the topic. Checking: 5 × 13 − 3 = 62, which matches. Deal with the adding and subtracting before the multiplying and dividing. It is the reverse of the order you would use to work the expression out.
The answer is D. Undo the operations in reverse order. The 3 was taken away last, so add it first: 62 + 3 = 65, so 5x = 65. Then undo the multiplication: 65 ÷ 5 = 13, so x = 13. Whatever is done to one side must be done to the other — that is the only rule in the topic. Checking: 5 × 13 − 3 = 62, which matches. Deal with the adding and subtracting before the multiplying and dividing. It is the reverse of the order you would use to work the expression out.
Grace buys some packs of stickers. Each pack holds 9 stickers, and Grace already had 8 stickers at home. That makes 71 stickers altogether. How many packs did Grace buy?
Let n be the number of packs. Each pack holds 9, so the packs give 9n, and the 8 already at home are added on: 9n + 8 = 71. Take the 8 off both sides: 9n = 71 − 8 = 63. Then divide by 9: n = 63 ÷ 9 = 7. Dividing 71 by 9 straight away gives 8 and quietly counts the 8 already at home as though they came in packs. Look for the amount that is there whatever happens — it gets added on, not multiplied.
The answer is C. Let n be the number of packs. Each pack holds 9, so the packs give 9n, and the 8 already at home are added on: 9n + 8 = 71. Take the 8 off both sides: 9n = 71 − 8 = 63. Then divide by 9: n = 63 ÷ 9 = 7. Dividing 71 by 9 straight away gives 8 and quietly counts the 8 already at home as though they came in packs. Look for the amount that is there whatever happens — it gets added on, not multiplied.
Solve 6x + 4 = 58.
Undo the operations in reverse order. The 4 was added last, so subtract it first: 58 − 4 = 54, so 6x = 54. Then undo the multiplication: 54 ÷ 6 = 9, so x = 9. Whatever is done to one side must be done to the other — that is the only rule in the topic. Checking: 6 × 9 + 4 = 58, which matches. Keep the equals signs lined up underneath each other. It makes a lost step visible.
The answer is B. Undo the operations in reverse order. The 4 was added last, so subtract it first: 58 − 4 = 54, so 6x = 54. Then undo the multiplication: 54 ÷ 6 = 9, so x = 9. Whatever is done to one side must be done to the other — that is the only rule in the topic. Checking: 6 × 9 + 4 = 58, which matches. Keep the equals signs lined up underneath each other. It makes a lost step visible.
Solve 2x + 16 = 38.
Undo the operations in reverse order. The 16 was added last, so subtract it first: 38 − 16 = 22, so 2x = 22. Then undo the multiplication: 22 ÷ 2 = 11, so x = 11. Whatever is done to one side must be done to the other — that is the only rule in the topic. Checking: 2 × 11 + 16 = 38, which matches. Keep the equals signs lined up underneath each other. It makes a lost step visible.
The answer is C. Undo the operations in reverse order. The 16 was added last, so subtract it first: 38 − 16 = 22, so 2x = 22. Then undo the multiplication: 22 ÷ 2 = 11, so x = 11. Whatever is done to one side must be done to the other — that is the only rule in the topic. Checking: 2 × 11 + 16 = 38, which matches. Keep the equals signs lined up underneath each other. It makes a lost step visible.
Solve 9x + 8 = 116.
Undo the operations in reverse order. The 8 was added last, so subtract it first: 116 − 8 = 108, so 9x = 108. Then undo the multiplication: 108 ÷ 9 = 12, so x = 12. Whatever is done to one side must be done to the other — that is the only rule in the topic. Checking: 9 × 12 + 8 = 116, which matches. Deal with the adding and subtracting before the multiplying and dividing. It is the reverse of the order you would use to work the expression out.
The answer is B. Undo the operations in reverse order. The 8 was added last, so subtract it first: 116 − 8 = 108, so 9x = 108. Then undo the multiplication: 108 ÷ 9 = 12, so x = 12. Whatever is done to one side must be done to the other — that is the only rule in the topic. Checking: 9 × 12 + 8 = 116, which matches. Deal with the adding and subtracting before the multiplying and dividing. It is the reverse of the order you would use to work the expression out.
Solve 2x + 8 = 18.
Undo the operations in reverse order. The 8 was added last, so subtract it first: 18 − 8 = 10, so 2x = 10. Then undo the multiplication: 10 ÷ 2 = 5, so x = 5. Whatever is done to one side must be done to the other — that is the only rule in the topic. Checking: 2 × 5 + 8 = 18, which matches. Always substitute your answer back into the original. An equation checks itself in seconds.
The answer is C. Undo the operations in reverse order. The 8 was added last, so subtract it first: 18 − 8 = 10, so 2x = 10. Then undo the multiplication: 10 ÷ 2 = 5, so x = 5. Whatever is done to one side must be done to the other — that is the only rule in the topic. Checking: 2 × 5 + 8 = 18, which matches. Always substitute your answer back into the original. An equation checks itself in seconds.
Aisha buys some bags of marbles. Each bag holds 5 marbles, and Aisha already had 13 marbles at home. That makes 28 marbles altogether. How many bags did Aisha buy?
Let n be the number of bags. Each bag holds 5, so the bags give 5n, and the 13 already at home are added on: 5n + 13 = 28. Take the 13 off both sides: 5n = 28 − 13 = 15. Then divide by 5: n = 15 ÷ 5 = 3. Dividing 28 by 5 straight away gives 6 and quietly counts the 13 already at home as though they came in bags. Write the equation before solving anything. Turning the words into symbols is the part being tested.
The answer is C. Let n be the number of bags. Each bag holds 5, so the bags give 5n, and the 13 already at home are added on: 5n + 13 = 28. Take the 13 off both sides: 5n = 28 − 13 = 15. Then divide by 5: n = 15 ÷ 5 = 3. Dividing 28 by 5 straight away gives 6 and quietly counts the 13 already at home as though they came in bags. Write the equation before solving anything. Turning the words into symbols is the part being tested.
Solve 4x + 10 = 54.
Undo the operations in reverse order. The 10 was added last, so subtract it first: 54 − 10 = 44, so 4x = 44. Then undo the multiplication: 44 ÷ 4 = 11, so x = 11. Whatever is done to one side must be done to the other — that is the only rule in the topic. Checking: 4 × 11 + 10 = 54, which matches. Deal with the adding and subtracting before the multiplying and dividing. It is the reverse of the order you would use to work the expression out.
The answer is D. Undo the operations in reverse order. The 10 was added last, so subtract it first: 54 − 10 = 44, so 4x = 44. Then undo the multiplication: 44 ÷ 4 = 11, so x = 11. Whatever is done to one side must be done to the other — that is the only rule in the topic. Checking: 4 × 11 + 10 = 54, which matches. Deal with the adding and subtracting before the multiplying and dividing. It is the reverse of the order you would use to work the expression out.
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