Mary’s and Bob’s ages combined are twice Jane’s age. Mary is years older than Bob. Jane’s age plus Bob’s age is years. How old are they?

Source: NCTM Mathematics Teacher, September 2006

**Solution
**Let , and represent the ages of Bob, Jane, and Mary respectively.

Add Eq. and Eq.

——————

Add Eq. and Eq.

——————

Substitute the value of in Eq. into Eq.

Jane’s age equals .

Substitute the value of Jane’s age into Eq.

Mary’s age equals .

Substitute the value of Jane’s age into Eq.

Bob’s age equals .

**Answer**: Bob is , Jane , Mary