A household keeps a note of two categories of spending to see where its money goes. It spends \(x\) pounds on clothes and \(y\) pounds on books over a fortn...
Question 1 Report
A household keeps a note of two categories of spending to see where its money goes. It spends \(x\) pounds on clothes and \(y\) pounds on books over a fortnight, and the amounts fit the two equations below.
\(x + y = 13\)
\(3x - 2y = 14\)
Work out the amount spent on clothes and the amount spent on books. (3)
Answer Details
The first equation rearranges directly to give \(y\) in terms of \(x\).
From \(x + y = 13\), \(y = 13 - x\). [1 mark]
Substituting into \(3x - 2y = 14\) gives \(3x - 2(13 - x) = 14\), so \(3x - 26 + 2x = 14\), giving \(5x = 40\) and \(x = 8\). [1 mark]
Then \(y = 13 - 8 = 5\). The household spends £8 on clothes and £5 on books. [1 mark]
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