Question

the sum of the ages of a man and his wife is 96 years. the man is 6 years older than his wife, how old is his wife

Answer 1

Answer:

Answer

Let the couple have x children.

Let the age of the man be M years and the age of wife of W years and the total age of the children be C years.

By the first condition, M+W=6C ...(1)

Two years ago, man's age =(M−2).

wife's age =(W−2)

and total age of the children, =(C−2x) as there are x children,

(M−2)+(W−2)=10(C−2x)

M+N−4=10C−20x ...(2)

From, equation 1and2,

6C−10C+20x=4

−4C+20x=4

=>−C+5x=1 ...(3)

After 6 years, man's age =(M+6)

wife's age =(W+6)

and total age of children, =(C+6x) as there as x children

Given, (M+6)+(W+6)=3(C+6x)

=>M+W+12=3C+18x ...(4)

From equation 1 and 4,

6C+12=3C+18x

=>C−6x=−4 ...(5)

Solving equation 3 and 5, we get

x=3

Hence, the man and wife have 3 children