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e
Standard memberelopawn

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.

P
Standard memberPBE6
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.

T
Standard memberTHUDandBLUNDER

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

S
Standard memberSchumi

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.

r
Standard memberroyalchicken
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.

e
Standard memberelopawn

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.