Question

A babysitter is trying to determine the ages of three children: Jerome, Keenan, and Leitha. She knows the following facts about their ages: the sum of Jerome’s and Keenan’s ages is 18 years; the sum of Jerome’s and Leitha’s ages is 19 years; and the sum of Keenan’s and Leitha’s ages is 21 years. How old is Keenan?

Answer 1

Keenan is 10 years old.

Explanation

Suppose, the age of Jerome is $x$ years, age of Keenan is  $y$ years and age of Leitha is  $z$ years.

The sum of Jerome’s and Keenan’s ages is 18 years. So, the first equation is......

$x+y=18 ..................................... (1)$

The sum of Jerome’s and Leitha’s ages is 19 years. So, the second equation is.........

$x+z= 19 .............................(2)$

The sum of Keenan’s and Leitha’s ages is 21 years. So, the third equation is...........

$y+z= 21 .............................(3)$

First, we will just add all the equations. So, adding equation (1), (2) & (3), we will get......

$(x+y)+(x+z)+(y+z)=18+19+21\\ \\ 2(x+y+z)= 58\\ \\ x+y+z= 29 ................................(4)$

Now, subtracting equation (2) from equation (4), we will get......

$(x+y+z)-(x+z)=29-19\\ \\ x+y+z-x-z=10\\ \\ y=10$

So, the age of Keenan is 10 years.