Algebra and equations · Ages 11–12
Finding the original worksheet
Part of: Equations with brackets, decimals and fractions
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Finding the original worksheet
Algebra and equations · Ages 11–12
Numsprite
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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.
Part A: Working out and filling in (2 marks each)
1.? decreased by 20% = 160
Answer:
2.50% of ? = 125
Answer:
3.10% of ? = 5
Answer:
4.40% of ? = 12
Answer:
5.? increased by 5% = 420
Answer:
6.50% off is $250: was $?
Answer:
7.? increased by 60% = 96
Answer:
8.? increased by 15% = 23
Answer:
9.50% off is $60: was $?
Answer:
10.80% of ? = 320
Answer:
11.50% off is $180: was $?
Answer:
12.? decreased by 40% = 150
Answer:
Part B: Word problems (4 marks each)
13.After a 20% rise, a box of chocolates costs $360. What did it cost before the rise, in dollars?
Working:
Answer:
14.A bicycle is reduced by 20% and now sells for $496. What was its original price, in dollars?
Working:
Answer:
15.With 20% off, a backpack sells for $224. What was its original price, in dollars?
Working:
Answer:
16.A bicycle is reduced by 20% and now sells for $480. What was its original price, in dollars?
Working:
Answer:
17.After a 10% rise, a box of chocolates costs $132. What did it cost before the rise, in dollars?
Working:
Answer:
18.With 30% off, a backpack sells for $294. What was its original price, in dollars?
Working:
Answer:
Show the answers and working
Finding the original worksheet: Answers and working
Part A: Working out and filling in
1. 200 decreased by 20% = 160
Down 20% leaves 100% − 20% = 80% of the number, so the number before = 160 ÷ 80%: 160 × 100 = 16000, 16000 ÷ 80 = 200
2. 50% of 250 = 125
125 is 50% of the number, so the number = 125 ÷ 50%: 125 × 100 = 12500, 12500 ÷ 50 = 250
3. 10% of 50 = 5
5 is 10% of the number, so the number = 5 ÷ 10%: 5 × 100 = 500, 500 ÷ 10 = 50
4. 40% of 30 = 12
12 is 40% of the number, so the number = 12 ÷ 40%: 12 × 100 = 1200, 1200 ÷ 40 = 30
5. 400 increased by 5% = 420
Up 5% leaves 100% + 5% = 105% of the number, so the number before = 420 ÷ 105%: 420 × 100 = 42000, 42000 ÷ 105 = 400
6. 50% off is $250: was $500
50% off leaves 50% of the price, so the price = 250 ÷ 50%: 250 × 100 = 25000, 25000 ÷ 50 = 500
7. 60 increased by 60% = 96
Up 60% leaves 100% + 60% = 160% of the number, so the number before = 96 ÷ 160%: 96 × 100 = 9600, 9600 ÷ 160 = 60
8. 20 increased by 15% = 23
Up 15% leaves 100% + 15% = 115% of the number, so the number before = 23 ÷ 115%: 23 × 100 = 2300, 2300 ÷ 115 = 20
9. 50% off is $60: was $120
50% off leaves 50% of the price, so the price = 60 ÷ 50%: 60 × 100 = 6000, 6000 ÷ 50 = 120
10. 80% of 400 = 320
320 is 80% of the number, so the number = 320 ÷ 80%: 320 × 100 = 32000, 32000 ÷ 80 = 400
11. 50% off is $180: was $360
50% off leaves 50% of the price, so the price = 180 ÷ 50%: 180 × 100 = 18000, 18000 ÷ 50 = 360
12. 250 decreased by 40% = 150
Down 40% leaves 100% − 40% = 60% of the number, so the number before = 150 ÷ 60%: 150 × 100 = 15000, 15000 ÷ 60 = 250
Part B: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. After a 20% rise, a box of chocolates costs $360. What did it cost before the rise, in dollars? (Answer: 300 dollars)
The new price is 120% of the old: 360 ÷ 120% = 300
14. A bicycle is reduced by 20% and now sells for $496. What was its original price, in dollars? (Answer: 620 dollars)
The sale price is 80% of the original: 496 ÷ 80% = 620
15. With 20% off, a backpack sells for $224. What was its original price, in dollars? (Answer: 280 dollars)
The sale price is 80% of the original: 224 ÷ 80% = 280
16. A bicycle is reduced by 20% and now sells for $480. What was its original price, in dollars? (Answer: 600 dollars)
The sale price is 80% of the original: 480 ÷ 80% = 600
17. After a 10% rise, a box of chocolates costs $132. What did it cost before the rise, in dollars? (Answer: 120 dollars)
The new price is 110% of the old: 132 ÷ 110% = 120
18. With 30% off, a backpack sells for $294. What was its original price, in dollars? (Answer: 420 dollars)
The sale price is 70% of the original: 294 ÷ 70% = 420
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