A football league is agreeing next season's budget split between its youth academy and its senior team ahead of a board meeting. The annual sponsorship fund...
Question 1 Report
A football league is agreeing next season's budget split between its youth academy and its senior team ahead of a board meeting. The annual sponsorship fund is shared between them in the ratio 3:7, and the senior team receives \(\pounds12000\) more than the youth academy. Work out the total sponsorship fund. (4)
Answer Details
Because the two shares stay in the ratio \(3:7\), they can be written as multiples of one unknown, \(x\); the given difference between the shares turns this into a single equation for \(x\), from which the total fund follows.
Let one share of the ratio \(=x\), so the youth academy receives \(3x\) and the senior team receives \(7x\). The difference between them is: \[ 7x-3x=4x=12000 \] [2 marks]
\[ x=3000 \] [1 mark]
The total sponsorship fund is: \[ 10x=\pounds30000 \] [1 mark]
As a check, the youth academy receives \(3\times3000=\pounds9000\) and the senior team receives \(7\times3000=\pounds21000\); their difference is \(\pounds12000\) as required, and together they total \(\pounds30000\).
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