Percentages and ratio · Ages 13–14

Chains of sellers and offers worksheet

Part of: Percentages (II)

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Percentages and ratio · Ages 13–14

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

1.A wholesaler buys at $600 an item and sells to a shop at a 35% profit; the shop sells at a 25% profit. Shop price = $
Answer:
2.An item costs $500 to make. The maker sells to a wholesaler at a 10% profit, for $; the wholesaler to a shop at 20%, for $; the shop sells at 25%, for $.
Fill in each blank
Answer:
3.An item costs $200 to make. The maker sells to a wholesaler at a 50% profit, for $; the wholesaler to a shop at 25%, for $; the shop sells at 20%, for $.
Fill in each blank
Answer:
4.A wholesaler buys at $480 an item and sells to a shop at a 45% profit; the shop sells at a 20% profit. Shop price = $
Answer:
5.Buy two of an item and the second is 30% off: over the two, that is % off
Answer:
6."Buy 5, get 3 free": you pay for items and take , the same as a % discount.
Fill in each blank
Answer:
7.The maker makes 20%, the wholesaler 40% and the shop 50%. The shop price is % above the cost of making it
Answer:

13.A supermarket's drinks are "buy 2, get 1 free", marked $9.5 a bottle. Tsz-hin takes 6 bottles. How much is paid?
Working:
Answer:
14.An item passes through three sellers, each making 25%, so the shop price is 95.3125% above the cost of making it.
True or false?
Working:
Answer:
15.Four shops have different offers on the same item. Buying 20 of them, which offer is the best deal?
- A. 80% off every second one
- B. 30% off everything
- C. Buy 9, get 1 free
- D. Second one half price
Choose the right answer
Working:
Answer:
16.The shop price is $120; the shop made 25% and the wholesaler 20%. With the maker's price to the wholesaler $x, find x: put the steps in order.
- A. x × 1.5 = 120
- B. x = 80
- C. x × 1.2 × 1.25 = 120
- D. x = 120 ÷ 1.5
Write the letters in the right order
Working:
Answer:
17.A shop buys 100 items at $50 each and marks them 60% above cost. The first 40 sell at the marked price and the rest as "buy 3, get 1 free". What is the profit percentage overall?
Working:
Answer:
18.A handbag costs $500 to make. The maker sells it to an agent at a 50% profit, the agent to a shop at 25%, and the shop sells it for $1,312.5. The shop's cost = $, and its profit percentage = %.
Fill in each blank
Working:
Answer:

Show the answers and working

Chains of sellers and offers worksheet: Answers and working

1. 1012.5
600 × (1 + 35%) = 810, then 810 × (1 + 25%) = 1012.5; or in one go: 600 × 1.35 × 1.25 = 1012.5.
2. 550, 660, 825
Each seller's cost is the last one's price: 500 × 1.1 = 550, 550 × 1.2 = 660, 660 × 1.25 = 825.
3. 300, 375, 450
Each seller's cost is the last one's price: 200 × 1.5 = 300, 300 × 1.25 = 375, 375 × 1.2 = 450.
4. 835.2
480 × (1 + 45%) = 696, then 696 × (1 + 20%) = 835.2; or in one go: 480 × 1.45 × 1.2 = 835.2.
5. 15
Two items are 2 shares of the price, and only 1 share is 30% off: 30% ÷ 2 = 15%. "Second one half price" is 50% ÷ 2 = 25%.
6. 5, 8, 37.5
Pay for 5, take 8: the free ones are 38 = 37.5% of them.
7. 152
(1 + 20%) × (1 + 40%) × (1 + 50%) = 1 + 152%: the three sellers' rates multiply, they don't add.

8. D. $72.8
The wholesaler pays 40 × (1 + 40%) = 56; the shop pays 56 × (1 + 30%) = 72.8.
9. True
You pay for 9 and take 10: you pay 910 = 90%, so the discount is 110 = 10%.
10. True
You pay for 19 and take 20: you pay 1920 = 95%, so the discount is 120 = 5%.
11. B. $105.6
The wholesaler pays 80 × (1 + 20%) = 96; the shop pays 96 × (1 + 10%) = 105.6.
12. C. $80
Divide back, seller by seller: 192 ÷ (1 + 60%) = 120, 120 ÷ (1 + 50%) = 80.

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

13. 38 dollars
Every 3 bottles cost 2: 6 bottles are 2 lots, so 2 × 2 × 9.5 = 38.
14. True
Three sellers multiply: 1.25³ = 1 + 95.3125%, so 95.3125% above, not 3 × 25% = 75%.
15. A. 80% off every second one
Turn each offer into a discount: 10%, 25%, 30%, 40%. The biggest is the best deal.
16. C → A → D → B
The wholesaler's 20% is times 1.2, the shop's 25% times 1.25: form the equation, multiply the factors, then divide both sides by 1.5.
17. 36%
Marked price 80; takings = 40 × 80 + 60 × 80 × 33 + 1 = 6800, cost 100 × 50 = 5000; (6800 − 5000) ÷ 5000 × 100% = 36%.
18. 937.5, 40
The shop's cost = 500 × (1 + 50%) × (1 + 25%) = 937.5; its profit percentage = (1312.5 − 937.5) ÷ 937.5 × 100% = 40%.

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