Henry Ernest Dudeney/Modern Puzzles/189 - Weighing the Baby/Solution
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Modern Puzzles by Henry Ernest Dudeney: $189$
- Weighing the Baby
- There was a family group at the automatic weighing machine, trying to weigh the baby.
- Whenever they put the baby on the machine, she always yelled and rolled off,
- while the father was holding off the dog, who always insisted on being included in the operations.
- At last the man, with the baby and Fido, were on the machine together.
- The dial read $180$ pounds.
- The man turned to his wife and said,
- What was the actual weight of the baby?
Solution
The baby weighs $30$ pounds.
The man weighs $141$ pounds, and Fido weighs $9$ pounds.
Proof
Let $m$, $b$ and $F$ be the weights of man, baby and Fido respectively.
We have:
\(\text {(1)}: \quad\) | \(\ds m + b + F\) | \(=\) | \(\ds 180\) | |||||||||||
\(\text {(2)}: \quad\) | \(\ds m + b\) | \(=\) | \(\ds F + 162\) | |||||||||||
\(\text {(3)}: \quad\) | \(\ds F\) | \(=\) | \(\ds b - b \times {70} {100}\) | |||||||||||
\(\ds \) | \(=\) | \(\ds \dfrac {3 b} {10}\) | ||||||||||||
\(\ds \leadsto \ \ \) | \(\ds F\) | \(=\) | \(\ds 18 - F\) | $(1) - (2)$ | ||||||||||
\(\ds \leadsto \ \ \) | \(\ds F\) | \(=\) | \(\ds 9\) | simplifying | ||||||||||
\(\ds \leadsto \ \ \) | \(\ds b\) | \(=\) | \(\ds 9 \times \dfrac {10} 3\) | substituting for $F$ in $(3)$ | ||||||||||
\(\ds \) | \(=\) | \(\ds 30\) | simplifying | |||||||||||
\(\ds \leadsto \ \ \) | \(\ds m + 30 + 9\) | \(=\) | \(\ds 180\) | substituting for $F$ and $b$ in $(1)$ | ||||||||||
\(\ds \leadsto \ \ \) | \(\ds m\) | \(=\) | \(\ds 141\) | simplifying |
$\blacksquare$
Sources
- 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Solutions: $189$. -- Weighing the Baby
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $99$. Weighing the Baby