Equations and inequalities · Ages 14–15

Word problems with inequalities worksheet

Part of: Linear inequalities in one unknown

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Equations and inequalities · Ages 14–15

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

1.Saving $45 a week, at least how many weeks does it take to have at least $750?
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2.With $67, at most how many pens at $8 each can be bought?
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3.With $82, at most how many pens at $6 each can be bought?
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4.Saving $30 a week, at least how many weeks does it take to have at least $500?
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5.5 times a number, take away 12, is not less than 29. What is the least whole number it can be?
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6.A lift carries at most 630 kg. A 63 kg delivery worker rides with boxes of 34 kg each. At most how many boxes can go in?
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7.A lift carries at most 1000 kg. A 58 kg delivery worker rides with boxes of 15 kg each. At most how many boxes can go in?
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8.A rectangular flower bed is 11 m longer than it is wide, and is to be fenced with no more than 33 m of fencing. If its width is a whole number of metres, at most how wide can it be?
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9.A gym charges two ways: plan A, $47 a visit; plan B, $400 a month plus $10 a visit. At least how many visits a month make plan B cheaper than A?
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10.A rectangular flower bed is 6 m longer than it is wide, and is to be fenced with no more than 77 m of fencing. If its width is a whole number of metres, at most how wide can it be?
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13.At a bookshop, non-members pay $141 a book; members pay $101 a book but first pay a $500 yearly fee. At least how many books in a year make membership cost less in all?
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14.Wai has $230 and saves $30 a week, aiming for at least $1,350 for a bike. With x weeks: 230 + 30x ≥ 1350, 30x ≥ , so it takes at least weeks.
Fill in each blank
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15.To make the running team, the average of four 400 m runs must be under 78 seconds. Ching's first three took 77, 75 and 82 seconds. At most how many whole seconds can the fourth take?
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16.A lift takes at most 630 kg. 5 passengers weigh 325 kg in all, and boxes of 30 kg each go in too. With x boxes: 325 + 30x ≤ 630, 30x ≤ , so at most boxes can go in.
Fill in each blank
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17.To make the running team, the average of four 400 m runs must be under 90 seconds. Ching's first three took 91, 92 and 93 seconds. At most how many whole seconds can the fourth take?
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18.A lift takes at most 600 kg. 8 passengers weigh 520 kg in all, and boxes of 17 kg each go in too. With x boxes: 520 + 17x ≤ 600, 17x ≤ , so at most boxes can go in.
Fill in each blank
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Show the answers and working

Word problems with inequalities worksheet: Answers and working

1. 17 weeks
With x weeks: 45x ≥ 750, x ≥ 75045. It must be whole, so round up: at least 17 weeks.
2. 8 pens
With x pens: 8x ≤ 67, x ≤ 678. A count is whole, so round down: at most 8.
3. 13 pens
With x pens: 6x ≤ 82, x ≤ 826. A count is whole, so round down: at most 13.
4. 17 weeks
With x weeks: 30x ≥ 500, x ≥ 50030. It must be whole, so round up: at least 17 weeks.
5. 9
With the number x: 5x − 12 ≥ 29, 5x ≥ 41, x ≥ 415. The least whole number from there is 9.
6. 16 boxes
With x boxes: 63 + 34x ≤ 630, 34x ≤ 567, x ≤ 56734. Round down: at most 16 boxes.
7. 62 boxes
With x boxes: 58 + 15x ≤ 1000, 15x ≤ 942, x ≤ 94215. Round down: at most 62 boxes.
8. 2 m
With width x m the length is (x + 11) m: 2(x + x + 11) ≤ 33, 4x + 22 ≤ 33, 4x ≤ 11, x ≤ 114. Round down: at most 2 m.
9. 11 visits
With x visits: 400 + 10x < 47x, 400 < 37x, x > 40037. The least whole number above that is 11.
10. 16 m
With width x m the length is (x + 6) m: 2(x + x + 6) ≤ 77, 4x + 12 ≤ 77, 4x ≤ 65, x ≤ 654. Round down: at most 16 m.

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

13. 13 books
With x books: 500 + 101x < 141x, 500 < (141 − 101)x, x > 500141 − 101. The least whole number above that is 13.
14. 1,120, 38
30x ≥ 1350 − 230 = 1120, x ≥ 112030. Weeks are whole, so round up: at least 38.
15. 77 seconds
With x seconds for the fourth: 77 + 75 + 82 + x4 < 78, 234 + x < 312, x < 312 − 234. The boundary itself is out, so at most 77.
16. 305, 10
30x ≤ 630 − 325 = 305, x ≤ 30530. Boxes are whole, so round down: at most 10.
17. 83 seconds
With x seconds for the fourth: 91 + 92 + 93 + x4 < 90, 276 + x < 360, x < 360 − 276. The boundary itself is out, so at most 83.
18. 80, 4
17x ≤ 600 − 520 = 80, x ≤ 8017. Boxes are whole, so round down: at most 4.

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