SP001 Maths Paper 2 - Question 16

Amy spent $\dfrac{4}{9}$ of her money on $39$ cashew nuts and $85$ peanuts.
The price of one cashew nut was $5$ times as much as the price of one peanut.
She then used $\dfrac{1}{7}$ of her money to buy more cashew nuts.
She spent a total of $\$28.50$ on all the cashew nuts.
How much did she spend on the peanuts?

Ans: $______________ [5]

Answer

maxloo · 30 Jun 2026, 14:18 · official answer

First, setup a table of proportions.
Let $p$ be the price of one peanut and $5p$ be the price of one cashew nut.
LCM of 9 and 7 = 63
So, we can let the total amount of money Amy has be 630 units.
Also, let Amy spend $\dfrac{1}{7}$ of her money to buy $n$ more cashew nuts.

cashew nuts price	peanuts price	total spent
$39$ $\times$ $5p$	$85$ $\times$ $p$	$\dfrac{4}{9}$ $\times$ $630$ = $280\ units$
$n$ $\times$ $5p$		$\dfrac{1}{7}$ $\times$ $630$ = $90\ units$

Since $39$ $\times$ $5p$ + $85$ $\times$ $p$	= $280\ units$
$p$	= $1\ unit$
So, $n$ $\times$ $5p$	= $90\ units$ = $90p$
$n$	= $18$

Total amount spent on cashew nuts	= $(39 + 18) × 5p$ = $28.5$
$p$	= $\$0.10$
Amount spend on peanuts	= $85$ $\times$ $p$
	= $\boxed{\$8.50}$