Amara receives a monthly allowance. She spends \(\frac{2}{5}\) of it on transport, then spends \(\frac{1}{4}\) of what remains on lunches, and saves the res...
Question 1 Report
Amara receives a monthly allowance. She spends \(\frac{2}{5}\) of it on transport, then spends \(\frac{1}{4}\) of what remains on lunches, and saves the rest.
- Write down the fraction of her allowance remaining after paying for transport. (1)
- Work out the fraction of her original allowance spent on lunches. (1)
- Show that the fraction of her original allowance she saves is \(\frac{9}{20}\). (1)
- Her allowance is \(\pounds160\). Work out how much she saves. (1)
Answer Details
This question applies a fraction of a fraction to a whole, tracking how much of an original amount is used at each stage before finding what remains.
After spending \(\dfrac{2}{5}\) on transport, the remaining fraction is:
\[1 - \dfrac{2}{5} = \dfrac{3}{5}\][1 mark]
Lunches cost \(\dfrac{1}{4}\) of what remains, which is \(\dfrac{1}{4}\) of the original allowance's \(\dfrac{3}{5}\):
\[\dfrac{1}{4} \times \dfrac{3}{5} = \dfrac{3}{20}\][1 mark]
The fraction saved is what remains after transport, minus what is spent on lunches:
\[\dfrac{3}{5} - \dfrac{3}{20} = \dfrac{12}{20} - \dfrac{3}{20} = \dfrac{9}{20}\]as required [1 mark].
- \[\dfrac{9}{20} \times £160 = £72\]
[1 mark]
The lunch fraction in part (b) is taken of the remaining \(\dfrac{3}{5}\), not of the whole original allowance, which is why "\(\dfrac{1}{4}\) of what remains" must be multiplied by \(\dfrac{3}{5}\) rather than used on its own.
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