Henry Ernest Dudeney/Puzzles and Curious Problems/297 - Mixing the Wine/Solution
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Puzzles and Curious Problems by Henry Ernest Dudeney: $297$
- Mixing the Wine
- A glass is one-third full of wine,
- and another glass, with equal capacity, is one-fourth full of wine.
- Each is filled with water and their contents mixed in a jug.
- Half of the mixture is poured into one of the glasses.
- What proportion of this is wine and what part water?
Solution
- $7$ parts wine to $17$ parts water.
Proof
Let $c$ be the capacity of one glass.
After they have been filled with water:
- the first one contains $\dfrac {4 c} {12}$ of wine
- the second one contains $\dfrac {3 c} {12}$ of wine.
In the jug together, there is $\dfrac {7 c} {12}$ of wine out of a total of $2 c$ of liquid.
When poured into one of the glasses, there is then $\dfrac 1 2 \times \dfrac {7 c} {12} = \dfrac {7 c} {24}$ of wine.
As this is in a container of capacity $c$, the ratio of wine to water is $\dfrac {7 c} {24} \div \dfrac {24 - 7 c} {24} = \dfrac 7 {17}$.
$\blacksquare$
Sources
- 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solutions: $297$. -- Mixing the Wine
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $408$. Mixing the Wine