The table shows how a football club's income is split between two sources, and the percentage increase in each source this year. Source Share of income Incr...
Question 1 Report
The table shows how a football club's income is split between two sources, and the percentage increase in each source this year.
| Source | Share of income | Increase this year |
|---|---|---|
| Ticket sales | 70% | 15% |
| Merchandise sales | 30% | 25% |
- Work out the overall percentage increase in the club's total income. (4)
- State whether the overall increase is closer to the ticket sales increase or the merchandise sales increase, and explain why in terms of the table. (1)
Answer Details
This question tests the weighted-average method for combining percentage increases in different proportions of a total, which is more general than the compound-multiplier method used when a single quantity changes twice.
Ticket sales make up \(70\%\) of income and rose by \(15\%\); merchandise makes up \(30\%\) of income and rose by \(25\%\). The overall percentage increase in total income is the weighted average of the two increases, weighted by their share of income:
\[(0.7 \times 15) + (0.3 \times 25) = 10.5 + 7.5 = 18\%\][4 marks]
The overall increase of \(18\%\) is closer to the merchandise sales increase of \(25\%\) than a simple average of \(15\%\) and \(25\%\) (which would be \(20\%\)) might suggest at first glance, but comparing \(18\%\) directly to each source, it sits closer to the ticket sales increase of \(15\%\), because ticket sales make up the larger share (\(70\%\)) of the club's income [1 mark].
The overall percentage change is pulled towards whichever source contributes the greater share of the total, which is why the weights in part (a) must match the shares in the table exactly.
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