Gabriel is 7 years older than Brianna. In 3 years the sum of their ages will be 55. How old is Gabriel now?

Question

Gabriel is 7 years older than Brianna. In 3 years the sum of their ages will be 55. How old is Gabriel now?

Answer 1

Hi Chelsea, the following is my method for solving the problem.

Let B = Brianna's age

Let G = Gabriel's age

Gabriel is 7 years older than Brianna

B + 7 = G

In 3 years, their ages will equal 55

(B + 3) + (G + 3) = 55

1. First substitute the equation for G into the other equation

(B + 7 + 3) + (B + 3) = 55 Now solve for B

B + 10 + B + 3 = 55

2B + 13 = 55

- 13. - 13

2B = 42

Divide both sides by 2

B = 21

Now plug B into original equation

B + 7 = G

21 + 7 = 28

G = 28

So Brianna's age is 21 and Gabriel's age is 28

Answer 2

Let the age of Gabriel be G and age of Brianna be B

G = B + 7

(G + 3) + (B + 3) = 55

Rearrange the equation:

G - B = 7

G + B = 49

Add both equations:

2G = 7 + 49

G = 56/2

G = 28