Equations and inequalities · Ages 12–13

Word problems with equations worksheet

Part of: Linear equations in one unknown

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Equations and inequalities · Ages 12–13

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Name:Date:Score:／48

Write each answer in the space. For word problems, show your working and write a sentence answer.

1.May buys 4 identical notebooks for $40 in all. With $x for one, the equation is 4x = 40, so x = .
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2.Tsz-hin has some stamps, is given 13 more, and then has 22. Say he had x at first: x + = 22, x = .
Fill in each blank
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3.Ka-lok has 3 times May's, 100 in all. May's is x: x = 100, x = .
Fill in each blank
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4.Ka-yan has some hair clips, is given 10 more, and then has 17. Say she had x at first: x + = 17, x = .
Fill in each blank
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5.18 coins, $5 and $2, $39 in all. 5x + 2(18 − x) = 39, 3x + = 39, x = .
Fill in each blank
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6.Ka-yee has 19 marbles, Ka-lok has 7. How many must Ka-yee give Ka-lok to match?
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7.Dad is 31 and his child is 7. In how many years will Dad be 3 times the child's age?
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8.Tsz-ching has 27 marbles, Ka-lok has 21. How many must Tsz-ching give Ka-lok to match?
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9.9 coins, $5 and $2, $42 in all. 5x + 2(9 − x) = 42, 3x + = 42, x = .
Fill in each blank
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10.Mum 42, child 15. How many years ago was she 4 times the child's age?
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11.Ka-yee has 40 books, Ka-lok 4. How many to give for 3 times Ka-lok's?
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13.Mum is 2 times her child's age; 9 years ago, 3 times. How old is the child?
Working:
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14.+7 right, −4 wrong, 30 goes, 67 points. With x right: 11x − = 67, x = .
Fill in each blank
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15.Ka-lok, Chi-keung: 57 in all. Ka-lok gives 4, then has 2 times Chi-keung's. How many at first?
Working:
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16.Mum: 26 years older, 3 times her child's age. 3x − x = 26, x = 26, x = .
Fill in each blank
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17.A has 3 times B's books. Moving 18 from A to B evens them. How many had B?
Working:
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18.A, B and C have 101. A has 4 times B's, and C 11 more than B. How many has C?
Working:
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Show the answers and working

Word problems with equations worksheet: Answers and working

1. 10
4x = 40; divide both sides by 4: x = 40 ÷ 4 = 10. Check: 4 notebooks at $10 make $40.
2. 13, 9
What he had plus the 13 given is 22: x + 13 = 22. Take 13 from both sides: x = 9.
3. 4, 25
3x + x = 4x, 4x = 100, x = 25.
4. 10, 7
What she had plus the 10 given is 17: x + 10 = 17. Take 10 from both sides: x = 7.
5. 36, 1
2 × 18 = 36; 3x = 39 − 36 = 3, x = 1. Supposing all were $2 gives the same: $3 short, $3 a swap.
6. 6 marbles
19 − x = 7 + x, 2x = 12, x = 6. Each one given closes the gap by 2.
7. 5 years
31 + x = 3(7 + x) gives x = 5. Check: in 5 years, 31 + 5 and 7 + 5.
8. 3 marbles
27 − x = 21 + x, 2x = 6, x = 3. Each one given closes the gap by 2.
9. 18, 8
2 × 9 = 18; 3x = 42 − 18 = 24, x = 8. Supposing all were $2 gives the same: $24 short, $3 a swap.
10. 6 years
42 − x = 4(15 − x) gives x = 6. Years ago: take x off both ages.
11. 7 books
40 − x = 3(4 + x) gives x = 7. Both change: Ka-yee loses x, Ka-lok gains x.

12. False
5x + 2(18 − x) = 74 must give a whole x: 74 − 2 × 18 must divide by 3. A number of coins can't be a fraction.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 18 years old
2x − 9 = 3(x − 9) gives x = 18, and Mum is 36.
14. 120, 17
7x − 4(30 − x) = 67. 4 × 30 = 120; a minus before the bracket makes −4 × (−x) = +4x, hence 11x. x = 17.
15. 42 stamps
x − 4 = 2(57 − x + 4) gives x = 42. The total stays 57: Chi-keung had 15.
16. 2, 13
3x − x = 2x, 2x = 26, x = 13.
17. 18 books
3x − 18 = x + 18, so 2x = 36, x = 18. Moving 18 closes the gap by 36.
18. 26 sweets
Choosing B as x is easiest: 4x + x + (x + 11) = 101, 6x + 11 = 101, x = 15. C has 26.

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