Question

My brainy brother and sister added their ages together and got 15. When they multiplied their ages together, they got 54. How old is the older one between the two of them?

Answer 1

Given:

Sum of ages of brother and sister = 15

Product of their ages = 54

To find:

How old is the older one between the two of them?

Solution:

Let x be the age of brother and y be the age of sister.

Sum of ages of brother and sister = 15

$x+y=15$

$x=15-y$                ...(i)

Product of their ages = 54

$xy=54$

$(15-y)y=54$                [Using (i)]

$15y-y^2=54$

$0=54-15y+y^2$

Splitting the middle term, we get

$54-15y+y^2=0$

$54-9y-6y+y^2=0$

$9(6-y)-y(6-y)=0$

$(6-y)(9-y)=0$

Using zero product property, we get

$(6-y)=0\text{ and }(9-y)=0$

$y=6\text{ and }y=9$

If $y=6$, then using (i), we get

$x=15-6$

$x=9$

If $y=9$, then using (i), we get

$x=15-9$

$x=6$

Therefore, the age of older one is 9, the age of younger one is 6 and the difference between their ages is 3.