Henry Ernest Dudeney/Puzzles and Curious Problems/30 - Subscriptions/Solution

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