A household splits its monthly leftover income into two pots to help it save for a holiday. It budgets \(x\) pounds for savings and \(y\) pounds for a treat...
Question 1 Report
A household splits its monthly leftover income into two pots to help it save for a holiday. It budgets \(x\) pounds for savings and \(y\) pounds for a treat fund, where the two amounts are connected as shown.
\(\frac{x}{2} + y = 10\)
\(x - y = 2\)
Give the amount saved and the amount put into the treat fund. (4)
Answer Details
The fraction in the first equation is cleared by multiplying through by 2 before the equations are combined.
Multiplying the first equation by 2 clears the fraction: \(x + 2y = 20\). [1 mark]
From the second equation, \(x = y + 2\); substituting gives \((y + 2) + 2y = 20\). [1 mark]
\(3y = 18\), so \(y = 6\), the amount put into the treat fund. [1 mark]
Then \(x = y + 2 = 8\), the amount saved. [1 mark]
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