Henry Ernest Dudeney/Puzzles and Curious Problems/30 - Subscriptions/Solution
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Puzzles and Curious Problems by Henry Ernest Dudeney: $30$
- Subscriptions
- Seven men agreed to subscribe towards a certain fund,
- and the first six gave $\pounds 10$ each.
- The other man gave $\pounds 3$ more than the average of the seven.
- What amount did the seventh man subscribe?
Solution
- $\pounds 13, 10 \shillings$
Proof
Let $T$ be the total amount subscribed.
Let $S$ be the amount contributed by the seventh man.
Then:
\(\ds T\) | \(=\) | \(\ds 60 + S\) | ... the first six gave $\pounds 10$ each | |||||||||||
\(\ds S\) | \(=\) | \(\ds \dfrac T 7 + 3\) | The other man gave $\pounds 3$ more than the average of the seven | |||||||||||
\(\ds \) | \(=\) | \(\ds \dfrac {60 + S} 7 + 3\) | ||||||||||||
\(\ds \leadsto \ \ \) | \(\ds 7 S\) | \(=\) | \(\ds 60 + S + 21\) | |||||||||||
\(\ds \leadsto \ \ \) | \(\ds 6 S\) | \(=\) | \(\ds 81\) | |||||||||||
\(\ds \leadsto \ \ \) | \(\ds S\) | \(=\) | \(\ds 13 \tfrac 1 2\) |
$\blacksquare$
Sources
- 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solutions: $30$. -- Subscriptions