What are their ages?

Question

The ages of Emily, Alyson, and Jodi are consecutive integers. The sum of their ages is 117. What are their ages?

Answer 1

First, define each of their ages in terms of x.

 

Emily's age = x;

Alyson's age = x + 1;

Jodi's age = x + 2;

 

The age of the girls must be consecutive integers, meaning they must be 3 whole numbers in order. For example, their ages could be 7, 8, 9, or 14, 15, 16, etc. If Emily is the youngest, we set her age to to x. This means Alyson will be one consecutive year older than Emily, giving you x + 1 as Alyson's age. Jodi will be one year older than Alyson, and two years older than Emily, giving you x + 2.

 

Now, to set up the equation:

 

x + (x + 1) + (x + 2) = 117

 

The sum of Emily's, Alyson's and Jodi's age is 117.

 

I added parentheses only to distinguish between the age of the girls.

 

x + x + 1 + x + 2 = 117 becomes:

 

3x + 3 = 117. Subtract 3 from both sides.

 

3x = 114. Divide each side by 3 to isolate x.

 

x = 38. 

 

X represents Emily's age, so Emily is 38, Alyson is 39, and Jodi is 40.