# Okay I've been working on this for 10 hours straight and cannot get it. This is a math problem from my teacher who just loves to add these frustrating math questions at the end of the worksheet. It says:

If you add the age of a man to the age of his wife you get a combined age of 91 years. He is now twice as old as she was when he was as old as she is now. How old are they?

I setup some algebra:
H = husband's age
W = wife's age

H + W = 91
H = 2(i don't know what to put here)

for the love of all gods mercy in the name of jesus and allah im on my knees will someone plz help me!

H + W = 91
The second depends on when it happened. Let a be years ago.
H=2(w -a) and finally,
H-a=w

Think on this. If you get stuck, repost.

you are the best thank you so much, it is clear now

Can someone tell me what their ages are?

that doesn't make sense

Phil is correct, that is not the right formula. The answer is he 52, she 39
when he was 39 she was 26. But I don't know how to get there using a formula.

## To find the ages of the husband and wife, we can solve the system of equations formed by the given information:

1) H + W = 91 (equation 1: the sum of their ages is 91)
2) H = 2(W - a) (equation 2: he is now twice as old as she was when he was as old as she is now)
3) H - a = W (equation 3: he was as old as she is now, a years ago)

To solve this system, we can start by substituting equation 3 into equation 2:

H = 2(W - a)
H = 2(W - H + a)
H = 2W - 2H + 2a
3H = 2W + 2a
W = (3H - 2a)/2 (equation 4: solved for W in terms of H and a)

Now, we have two equations with two unknowns, H and W. We can substitute equation 4 into equation 1 to eliminate W:

H + W = 91
H + (3H - 2a)/2 = 91
2H + 3H - 2a = 182
5H = 2a + 182
H = (2a + 182)/5 (equation 5: solved for H in terms of a)

We still have one variable, a, in equations 4 and 5. To find its value, we need to use equation 2: H = 2(W - a)

Substitute equation 4 into equation 2:

(2a + 182)/5 = 2(((3H - 2a)/2) - a)
(2a + 182)/5 = 2((3H/2) - 2a/2 - a)
(2a + 182)/5 = 2(3H/2 - 3a/2 - a)
(2a + 182)/5 = 3H - 3a/2 - 2a
(2a + 182)/5 = (6H - 3a - 4a)/2
(2a + 182)/5 = (6H - 7a)/2
4a + 364 = 10H - 14a
14a - 4a = 10H - 364
10a = 10H - 364
a = (10H - 364)/10
a = H - 36.4 (equation 6: solved for a in terms of H)

Now, we can substitute equation 6 into equation 5 to find H:

H = (2a + 182)/5
H = (2(H - 36.4) + 182)/5
H = (2H - 72.8 + 182)/5
5H = 2H + 109.2
3H = 109.2
H = 36.4

Finally, substitute H = 36.4 into equation 4 to find W:

W = (3H - 2a)/2
W = (3(36.4) - 2a)/2
W = (109.2 - 2a)/2
W = 54.6 - a

Since H = 36.4, we can substitute it into equation 3 to solve for a:

H - a = W
36.4 - a = 54.6 - a
0 = 54.6 - 36.4
a = 18.2

Therefore, the husband is 36.4 years old and the wife is 54.6 - 18.2 = 36.4 years old as well.