Henry Ernest Dudeney/Puzzles and Curious Problems/166 - Hens and Tens/Solution

Puzzles and Curious Problems by Henry Ernest Dudeney: $166$

Hens and Tens

If ten hen-pens cost ten and tenpence (that is, $10 \shillings 10 \oldpence$),

and ten hens and one hen-pen cost ten and tenpence,

what will ten hens without any hen-pens cost?

Solution

$9 \shillings 9 \oldpence$

Proof

Let $h$ pence be the cost of one hen.

Let $p$ pence be the cost of one hen-pen.

We have that:

$10 \shillings 10 \oldpence = 130 \oldpence$

Hence:

\(\ds 10 p\)

\(=\)

\(\ds 130\)

ten hen-pens cost ten and tenpence

\(\ds 10 h + p\)

\(=\)

\(\ds 130 \oldpence\)

ten hens and one hen-pen cost ten and tenpence

\(\ds \leadsto \ \ \)

\(\ds p\)

\(=\)

\(\ds 13\)

\(\ds \leadsto \ \ \)

\(\ds 10 h + 13\)

\(=\)

\(\ds 130\)

\(\ds \leadsto \ \ \)

\(\ds 10 h\)

\(=\)

\(\ds 117\)

Converting from pence into shillings and pence is all that remains to be done.

$\blacksquare$

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solutions: $166$. -- Hens and Tens