A swimming club's sponsorship money is shared between the junior squad and the senior squad in the ratio \(3:5\). The senior squad then donates \(\pounds 40...
Question 1 Report
A swimming club's sponsorship money is shared between the junior squad and the senior squad in the ratio \(3:5\). The senior squad then donates \(\pounds 40\) of its share to a local charity, leaving the two squads with exactly equal amounts.
- Taking the junior share as \(3k\) and the original senior share as \(5k\), form an equation in \(k\) from this condition. (2)
- Hence work out the total sponsorship money raised. (1)
Answer Details
Sharing money in a ratio means splitting the total into equal parts, \(k\), one part for each side of the ratio; a later change (here, a donation) then creates a new equation that can be solved to find the value of \(k\), and hence the actual amounts.
(a) The junior share is \( 3k \) and the senior share starts as \( 5k \). After donating \( £40 \), the senior share becomes \( 5k-40 \). Since the two squads then hold equal amounts, \( 3k = 5k-40 \) [2 marks].
(b) Subtracting \( 3k \) from both sides gives \( 0=2k-40 \), so \( 2k=40 \), giving \( k=20 \). The total sponsorship money raised is the sum of the two original shares, before the £40 donation left the squads' funds for charity: \( 3k+5k=8k=8(20)=£160 \) [1 mark].
Since the donation of £40 leaves the two squads' funds, the equal amount each squad holds afterwards (\(3k=60\) each) does not itself total the original £160 raised; the original ratio \(3k:5k\) is what must be added to recover the full amount raised before the donation was made.
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