FractionsStructured · 5 marks

Daniel had some money. He spent 35 of his money on 4 identical notebooks and 2 identical files at a stationery shop. He then spent 12 of his remaining money on a calculator. Each file cost $3 more than each notebook, and the calculator cost $7 more than each file.

What fraction of Daniel's money was spent on the calculator?
What was the total amount spent on the notebooks and files?
How much money did Daniel have at first?

Need a hint?

Find how many units the notebooks and files cost and how many the calculator costs. Then compare the two: how many calculators do the notebooks and files cost altogether?

Worked answer

(a) Remaining money = 1 − 35 = 25.
Calculator = 12 of 25 = 15 of Daniel's money.
(b) The notebooks and files cost 35 = 3 units, and the calculator costs 15 = 1 unit, so the notebooks and files cost 3 times as much as the calculator.
4 notebooks + 2 files = 6 notebooks + 2 × $3 = 6 notebooks + $6.
Calculator = file + $7 = notebook + $3 + $7 = 1 notebook + $10.
3 calculators = 3 notebooks + $30, and this equals 6 notebooks + $6.
So 3 notebooks = $30 − $6 = $24, and 1 notebook = $8.
Notebooks and files = 6 × $8 + $6 = $54.
(c) Calculator = $8 + $10 = $18, and this is 15 of Daniel's money.
Money at first = 5 × $18 = $90.

Answer: $90

The mistake this question tests

Habit

Fraction of a remainder

Many pupils think the calculator took 12 of the money, forgetting that the 12 is only of the remainder. The calculator is 12 of 25, which is 15.

How to fix it at home →

Daniel had some money. He spent 35 of his money on 4 identical notebooks and 2 identical files at a stationery shop. He then spent 12 of his remaining money on a calculator. Each file cost $3 more than each notebook, and the calculator cost $7 more than each file.

Worked answer

The mistake this question tests

Fraction of a remainder

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