An item costs $200 to make. The maker sells to a wholesaler at a 25% profit, for $□; the wholesaler to a shop at 40%, for $□; the shop sells at 40%, for $□. Fill in each blank

250, 350, 490. Each seller's cost is the last one's price: 200 × 1.25 = 250, 250 × 1.4 = 350, 350 × 1.4 = 490.

"Buy 9, get 1 free" is the same as a 90% discount. True or false?

False. You pay for 9 and take 10: you pay 9/10 = 90%, so the discount is 1/10 = 10%.

"Buy 3, get 1 free": you pay for □ items and take □, the same as a □% discount. Fill in each blank

3, 4, 25. Pay for 3, take 4: the free ones are 1/4 = 25% of them.

Percentages (II) · Ages 13–14

Chains of sellers and offers

Each seller's cost is the last one's price: multiply along.

How to do it

Method

Each seller's cost is the last one's price: multiply along

100 × 1.2 × 1.25 × 1.4 = 210

Another way

Seller by seller

100 → 120 → 150 → 210

In full

Goods go from a maker to a wholesaler, on to a shop, and then to a customer. Each seller's profit percentage is on that seller's cost, the last seller's price, so the factors multiply. The maker's cost is $100; it sells at a 20% profit to the wholesaler, who makes 25% selling to the shop, which makes 40% selling it on: one way, multiply, 100 × 1.2 × 1.25 × 1.4 = $210; another, seller by seller, 100 → 120 → 150 → 210. That is 110% added in all, not 20% + 25% + 40% = 85%. Back to the maker's cost: divide the last price back, seller by seller. An offer can be turned into a discount too: 'buy 3, get 1 free' pays for 3 and takes 4, paying 34 = 75%, a 25% discount; 'the second one half price' pays for 1.5 of 2, a discount of 0.5 ÷ 2 = 25%.

Worked examples

Have a go first, then open each one for the answer and the working.

Example 1
An item costs $200 to make. The maker sells to a wholesaler at a 25% profit, for $; the wholesaler to a shop at 40%, for $; the shop sells at 40%, for $.
Fill in each blank
Show the answer and working
Answer: 250, 350, 490
Each seller's cost is the last one's price: 200 × 1.25 = 250, 250 × 1.4 = 350, 350 × 1.4 = 490.
Example 2
"Buy 9, get 1 free" is the same as a 90% discount.
True or false?
Show the answer and working
Answer: False
You pay for 9 and take 10: you pay 910 = 90%, so the discount is 110 = 10%.
Example 3
"Buy 3, get 1 free": you pay for items and take , the same as a % discount.
Fill in each blank
Show the answer and working
Answer: 3, 4, 25
Pay for 3, take 4: the free ones are 14 = 25% of them.

Practice questions to try

Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.

1."Buy 3, get 1 free" is the same as a 75% discount.
True or false?
Answer:
2.A maker's cost is $50 an item. It sells at a 25% profit to a wholesaler, who sells on to a shop at a 20% profit. What does the shop pay an item?
- A. $72.5
- B. $62.5
- C. $60
- D. $75
Choose the right answer
Answer:
3.An item costs $200 to make. The maker sells to a wholesaler at a 20% profit, for $; the wholesaler to a shop at 10%, for $; the shop sells at 40%, for $.
Fill in each blank
Answer:
4."Buy 9, get 1 free": you pay for items and take , the same as a % discount.
Fill in each blank
Answer:
5.The maker makes 20%, the wholesaler 10% and the shop 25%. The shop price is % above the cost of making it
Answer:

All the answers

1. False
2. D. $75
3. 240, 264, 369.6
4. 9, 10, 10
5. 65

Free worksheet: Chains of sellers and offersWorking out, multiple choice and word problems, with answers and working, to print or save as a PDF

VIP practice notes and papers

Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.

Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
Practice paper: Set out in parts like a school paper, marked, with answers and full working

Start playingPlay and learn in the secondary world, Star Galaxy: animated methods, monster battles, a review of every mistake