Henry Ernest Dudeney/Puzzles and Curious Problems/150 - Sheep Sharing/Solution
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Puzzles and Curious Problems by Henry Ernest Dudeney: $150$
- Sheep Sharing
- An Australian farmer dies and leaves his sheep to his three sons.
- Alfred is to get $20$ per cent more than John,
- and $25$ per cent more than Charles.
- John's share is $3600$ sheep.
- How many sheep does Charles get?
Solution
Charles gets $3456$ sheep.
Proof
Let $A$, $J$ and $C$ be the number of sheep each of Alfred, John and Charles got respectively.
We have:
| \(\text {(1)}: \quad\) | \(\ds A\) | \(=\) | \(\ds J + \dfrac {20 J} {100} = \dfrac {6 J} 5\) | Alfred is to get $20$ per cent more than John, | ||||||||||
| \(\text {(2)}: \quad\) | \(\ds A\) | \(=\) | \(\ds C + \dfrac {25 J} {100} = \dfrac {5 C} 4\) | and $25$ per cent more than Charles. | ||||||||||
| \(\text {(3)}: \quad\) | \(\ds J\) | \(=\) | \(\ds 3600\) | John's share is $3600$ sheep. | ||||||||||
| \(\ds \leadsto \ \ \) | \(\ds A\) | \(=\) | \(\ds \dfrac {6 \times 3600} 5\) | substituting from $(3)$ into $(1)$ | ||||||||||
| \(\ds \) | \(=\) | \(\ds 4320\) | substituting from $(3)$ into $(1)$ | |||||||||||
| \(\ds \leadsto \ \ \) | \(\ds 4320\) | \(=\) | \(\ds \dfrac {5 \times C} 4\) | substituting into $(2)$ | ||||||||||
| \(\ds \leadsto \ \ \) | \(\ds C\) | \(=\) | \(\ds 3456\) | simplifying |
$\blacksquare$
Sources
- 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solutions: $150$. -- Sheep Sharing
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $222$. Sheep Sharing