A drinks stall keeps its paper cups in 15 stacks on a shelf. Every stack has the same number of cups, and the cups in a stack fit into one another. A stack of 7 cups is 27 cm tall.
- How many cups are there on the shelf?
- 2 cups are taken from each stack. These cups are used to make 6 new stacks, and each new stack is 21 cm tall. What is the height of one cup?
Need a hint?
Find how many cups are in each new stack. Then compare the 7-cup stack with the new stack to see how much height each extra cup adds.
Worked answer
- (a) Cups on the shelf = 15 × 7 = 105.
- (b) Cups taken away = 15 × 2 = 30.
- Each new stack has 30 ÷ 6 = 5 cups, and 5 cups are 21 cm tall.
- A stack of 7 cups is 27 cm. A stack of 5 cups is 21 cm.
- The extra 7 − 5 = 2 cups add 27 − 21 = 6 cm.
- Each extra cup adds 6 ÷ 2 = 3 cm, because cups fit into one another and only the rim shows.
- A stack of 7 cups = 1 whole cup + 6 extra cups, so 6 extra cups add 6 × 3 = 18 cm.
- Height of 1 cup = 27 − 18 = 9 cm.
The mistake this question tests
Calculation slip
Pupils divide 27 by 7 to get the height of one cup. The cups fit into one another, so each extra cup adds only a small amount to the height.
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