Henry Ernest Dudeney/Puzzles and Curious Problems/1 - The Money Bag/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $1$

The Money Bag

"A bag," said Rackbrane, when helping himself to the marmalade, "contained fifty-five coins consisting entirely of crowns and shillings,

and their total value was $\pounds 7, \ 3 \shillings 0 \oldpence$

How many coins were there of each kind?"

Solution

$22$ crowns and $33$ shillings.

Proof

Let $c$ and $s$ be the number of crowns and shillings respectively.

Recall that:

$1$ crown is worth $5$ shillings

$1$ pound is worth $20$ shillings.

Hence:

\(\text {(1)}: \quad\)

\(\ds 5 c + s\)

\(=\)

\(\ds 143\)

their total value was $\pounds 7, \ 3 \shillings 0 \oldpence$

\(\text {(2)}: \quad\)

\(\ds c + s\)

\(=\)

\(\ds 55\)

fifty-five coins consisting entirely of crowns and shillings

\(\ds \leadsto \ \ \)

\(\ds 4 c\)

\(=\)

\(\ds 88\)

$(1) - (2)$

\(\ds \leadsto \ \ \)

\(\ds c\)

\(=\)

\(\ds 22\)

\(\ds \leadsto \ \ \)

\(\ds s\)

\(=\)

\(\ds 55 - 22\)

\(\ds \)

\(=\)

\(\ds 33\)

$\blacksquare$

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solutions: $1$. -- The Money Bag