Question

Amy's age plus Betty's age is 29 years. Amy's plus Carl's age is 27 years. Betty's plus Carl's age is 22 years. What is the difference between the oldest child and the youngest child is?

Answer 1

Difference between age of oldest child and youngest child is 7 years

Solution:

Need to find difference between Oldest and youngest child.

Let assume Amy’s age be represented by variable A

And assume Betty’s age be represented by variable B

And assume Carl's age be represented by Variable C.

Lets first try to calculate each age from given equation.

So From Given information,

Amy's age plus Betty's age is 29 years  

A + B = 29      ------(1)

Amy's plus Carl's age is 27 years.  

A + C = 27      ------(2)  

Betty's plus Carl's age is 22 years.

B + C = 22      ------(3)

On subtracting equation (3) from (2) we get

(A + C) – (B + C) = 27 – 22

=> A – B = 5    ------(4)

On adding equation (1) and (4), we get

(A + B) + (A – B) = 29 + 5

=> 2A = 34

=> A = 17

From (1)

A + B = 29

=> 17 + B = 29

=> B = 29 – 17 = 12

From (3)

B + C = 22

=> 12 + C = 22

=> C = 22 -12 = 10

So Amy’s age A = 17, Betty’s age B = 12 and Carl’s age C = 10

So Youngest is Carl and Oldest in Amy

And difference between age of oldest child and youngest child = Amy age - Carl age

= 17 – 10 = 7 years