Henry Ernest Dudeney/Modern Puzzles/17 - Name their Wives

by : $17$

 * Name their Wives
 * A man left a legacy of $\pounds 1000$ to $3$ relatives and their wives.


 * The wives received together $\pounds 396$.
 * Jane received $\pounds 10$ more than Catherine,
 * and Mary received $\pounds 10$ more than Jane.


 * John Smith was given just as much as his wife,
 * Henry Snooks got half as much again as his wife,
 * and Tom Crowe received twice as much as his wife.


 * What was the Christian name of each man's wife?

Solution

 * Catherine is Mrs. John Smith
 * Jane is Mrs. Henry Snooks
 * Mary is Mrs. Tom Crowe.

Proof
Let $C$, $M$ and $J$ be the sizes of legacies of Catherine, Mary and Jane respectively.

We are given that:

Now we note that the total inherited by the husbands is $1000 - 396 = 604$.

Using the method of false position, we multiply $C$, $J$ and $M$ by $1$, $\dfrac 3 2$ and $2$ respectively, and sum them to see what we get.

Thus we find:


 * $122 + \dfrac 3 2 \times 132 + 2 \times 142 = 604$

and marvel that the first guess was spot on.

So:
 * Catherine is Mrs. John Smith
 * Jane is Mrs. Henry Snooks
 * Mary is Mrs. Tom Crowe.