A man is 5 years older than his wife, and the daughter age is half of the mother, and if you add the

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A man is 5 years older than his wife, and the daughter age is half of the mother, and if you add their ages is equal 100

Let the man's age be m. Let the wife's age be w. Let the daughter's age be d. We're given:

1. m = w + 5
2. d = 0.5m
3. d + m + w = 100

Rearrange equation 1 in terms of w my subtracting 5 from each side:

1. w = m - 5
2. d = 0.5m
3. d + m + w = 100

Substitute equation (1) and equation (2) into equation (3)
0.5m + m + m - 5 = 100

We type this equation into our search engine to solve for m and we get:
m = 42

Now, substitute m = 42 into equation 2 to solve for d:
d = 0.5(42)
d = 21

Now substitute m = 42 into equation 1 to solve for w:
w = 42 - 5
w = 37

To summarize our ages:

• Man (m) = 42 years old
• Daughter (d) = 21 years old
• Wife (w) = 37 years old