Algebra and equations · Ages 11–12

Solving word problems with equations worksheet

Part of: Equations with brackets, decimals and fractions

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Algebra and equations · Ages 11–12

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

1.Dad is 3 times as old as Tsz-ching, and their ages add up to 32. With x for Tsz-ching's age, the equation is x + 3x = 32. How old is Tsz-ching?
Answer:
2.A rectangle has an area of 50 cm² and a width of 4 cm. Let its length be x cm: 4x = 50. x =
Answer:
3.A rectangle is 5 cm longer than it is wide, and its perimeter is 44 cm. How wide is it, in cm?
Answer:
4.A triangle has an area of 37.5 cm² and a base of 5 cm. How tall is it, in cm?
Answer:
5.A rectangle is 2 cm longer than it is wide, and its perimeter is 66 cm. How wide is it, in cm?
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6.A square has the same perimeter as a rectangle 19 cm long and 4 cm wide. How long is a side of the square, in cm?
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7.Ka-yan buys 4 notebooks at the same price and a pencil case for 12 dollars, paying 84 dollars in all. With x dollars for one notebook, which equation is right?
- A. 4x + 12 = 84
- B. 4x = 84 + 12
- C. 4(x + 12) = 84
- D. x + 12 = 84
Choose the right answer
Answer:
8.10% of a number is 3. Let the number be x. Which equation is right?
- A. x − 10% = 3
- B. 3 × 10% = x
- C. x ÷ 10% = 3
- D. 10% × x = 3
Choose the right answer
Answer:
9.A rectangle is x cm long and 9 cm wide, with a perimeter of 44 cm. Which equation is right?
- A. x + 9 = 44
- B. 9x = 44
- C. 2(x + 9) = 44
- D. 2x + 9 = 44
Choose the right answer
Answer:
10.40% of a number is 10. Let the number be x. Which equation is right?
- A. 10 × 40% = x
- B. x ÷ 40% = 10
- C. 40% × x = 10
- D. x − 40% = 10
Choose the right answer
Answer:
11.A trapezium has an upper base of 10 cm, a height of 6 cm and an area of 45 cm². Its lower base is 15 cm.
True or false?
Answer:
12.A trapezium has an upper base of 7 cm, a height of 4 cm and an area of 22 cm². Its lower base is 11 cm.
True or false?
Answer:

13.Ka-yan uses exactly 28 m of rope to make a rectangle that is 3 times as long as it is wide. How wide is the rectangle, in metres?
Working:
Answer:
14.Adult tickets are $85 each and child tickets $45 each. A family buys 2 adult tickets and some child tickets for $260 in all. How many child tickets do they buy?
Working:
Answer:
15.Tsz-ching's dad is 5 times as old as Tsz-ching, and 44 years older. How old is Tsz-ching?
Working:
Answer:
16.A rectangular lawn is 24 m long with an area of 156 m². A rectangular path beside it is just as wide and 18 m long. What is the path's area, in m²?
Working:
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17.May gives 10% of her savings to charity, then spends $16 on a book, leaving $560. How much were her savings?
Working:
Answer:
18.A rectangular lawn is 18 m long with an area of 99 m². A rectangular path beside it is just as wide and 20 m long. What is the path's area, in m²?
Working:
Answer:

Show the answers and working

Solving word problems with equations worksheet: Answers and working

1. 8 years old
x + 3x are like terms: how many x is that altogether? Join them first.
x + 3x = 4x = 32, so x = 32 ÷ 4 = 8.
2. 12.5 cm
4x = 50. To find x, divide both sides by 4.
x = 50 ÷ 4 = 12.5.
3. 8.5 cm
Let the width be x cm, so the length is x + 5. Use perimeter = 2 × (length + width).
Let the width be x cm, so the length is x + 5: 2(x + x + 5) = 44; 2x + 5 = 22; 2x = 17; x = 8.5.
4. 15 cm
Triangle area = base × height ÷ 2. Let the height be x: 5 × x ÷ 2 = 37.5.
Let the height be x cm: 5 × x ÷ 2 = 37.5; 5x = 75; x = 15.
5. 15.5 cm
Let the width be x cm, so the length is x + 2. Use perimeter = 2 × (length + width).
Let the width be x cm, so the length is x + 2: 2(x + x + 2) = 66; 2x + 2 = 33; 2x = 31; x = 15.5.
6. 11.5 cm
First find the rectangle's perimeter, 2 × (19 + 4). The square's is the same.
Let the side be x cm: 4x = 2 × (19 + 4) = 46; x = 46 ÷ 4 = 11.5.

7. A. 4x + 12 = 84
4 notebooks cost 4x dollars. Add the pencil case: what should the total be?
4 notebooks cost 4x dollars; with the 12-dollar case that is 84: 4x + 12 = 84.
8. D. 10% × x = 3
“10% of the number” means 10% × x. Which equation says that equals 3?
“10% of the number” is 10% × x, and it equals 3: 10% × x = 3, x = 30.
9. C. 2(x + 9) = 44
Perimeter = 2 × (length + width). Put x and 9 into that.
Perimeter = 2 × (length + width): 2(x + 9) = 44.
10. C. 40% × x = 10
“40% of the number” means 40% × x. Which equation says that equals 10?
“40% of the number” is 40% × x, and it equals 10: 40% × x = 10, x = 25.
11. False
Trapezium area = (upper base + lower base) × height ÷ 2. Put in 15 for the lower base and see if the area is 45.
Let the lower base be x cm: (10 + x) × 6 ÷ 2 = 45, so 10 + x = 45 × 2 ÷ 6, x = 5.
12. False
Trapezium area = (upper base + lower base) × height ÷ 2. Put in 11 for the lower base and see if the area is 22.
Let the lower base be x cm: (7 + x) × 4 ÷ 2 = 22, so 7 + x = 22 × 2 ÷ 4, x = 4.

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

13. 3.5 m
Let the width be x m, so the length is 3x m. The rope is the perimeter: 2(3x + x) = 28.
Let the width be x m, so the length is 3x: 2(3x + x) = 28; 4x = 14; x = 3.5.
14. 2 tickets
Let it be x child tickets. Work out the 2 adult tickets first, then take that from 260.
Let it be x child tickets: 2 × 85 + 45x = 260; 45x = 260 − 170 = 90; x = 2.
15. 11 years
Let Tsz-ching be x, so Dad is 5x. How many more x is Dad than Tsz-ching?
Let Tsz-ching be x: 5x − x = 44, 4x = 44, x = 11.
16. 117 m²
The path is as wide as the lawn. Find the width from the lawn first: 24x = 156.
Let the width be x m: 24x = 156, x = 6.5; the path is 18 × 6.5 = 117 m².
17. 640 dollars
Let the savings be $x. After giving 10% away, what percentage of x is left?
Then think: how much was left before the book?
Let it be $x: x − 10% × x − 16 = 560; 90% × x = 576; x = 576 ÷ 90% = 640.
18. 110 m²
The path is as wide as the lawn. Find the width from the lawn first: 18x = 99.
Let the width be x m: 18x = 99, x = 5.5; the path is 20 × 5.5 = 110 m².

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