Ages

elopawn

Posers and Puzzles

25 Apr 05

elopawn

Joined: 21 Apr 05
Moves: 54

25 Apr 05

If the product of a woman's present age (W) and wedding age (w) is subtracted from the product of her husband's present age (M) and wedding age (m) and the result of this is added to (Wm-Mw) the result is 553. Find the present ages.

PBE6

Bananarama

False berry

Joined: 14 Feb 04
Moves: 28719

25 Apr 05

I'm assuming that you're looking for an integer solution. If so, the man is presently 43 and the woman is 36. They have been married for 16 years.

THUDandBLUNDER

Joined: 29 Feb 04
Moves: 22

25 Apr 05

2 edits

Originally posted by elopawn
If the product of a woman's present age (W) and wedding age (w) is subtracted from the product of her husband's present age (M) and wedding age (m) and the result of this is added to (Wm-Mw) the result is 553. Find the present ages.

Mm - Ww + Wm - Mw
= M(m - w) + W(m - w)
= (M + W)(m - w)

But M - m = W - w
So m - w = M - W

Hence (M + W)(M - W) = 553 = 79*7

M = 43
W = 36

Schumi

Dublin

Joined: 07 Feb 05
Moves: 8227

25 Apr 05

Originally posted by PBE6
They have been married for 16 years.

How do you get that? Seems to me that all you can get about their ages when married is the that he's 7 years older.

royalchicken

CHAOS GHOST!!!

Elsewhere

Joined: 29 Nov 02
Moves: 17317

25 Apr 05

Originally posted by Schumi
How do you get that? Seems to me that all you can get about their ages when married is the that he's 7 years older.

The current ages must sum to 79, and differ by 7.

elopawn

Joined: 21 Apr 05
Moves: 54

26 Apr 05

Originally posted by THUDandBLUNDER
Mm - Ww + Wm - Mw
= M(m - w) + W(m - w)
= (M + W)(m - w)

But M - m = W - w
So m - w = M - W

Hence (M + W)(M - W) = 553 = 79*7

M = 43
W = 36

Yep that's it. Good work.

If you still dont get it.....

We have Mm-Ww+Wm-Mw = 553
Hence M(m-w)+W(m-w) = 553
Therefore (M + W)(m - w) = 553 = 7*79

Let x be the number of years between the wedding and the present day. Then m = M-x, w = W-x and m-w = M-x-W+x = M-W

Hence (M + W)(M - W) = 7*79

Then either M+W = 553 ( this is not reasonable as the couple would be too old)

or M+W = 79

Then M-W = 7. Adding these gives 2M = 79+7 = 86 and M=43
Then W = 43 - 7 = 36

Basically what TB said. You should be able to get it now Schumi.