Question

Solve by using a system of two equations in two variables.

Six years ago, Joe Foster was two years more than five times as old as his daughter. Six years from now, he will be 11 years more than twice as old as she will be. How old is Joe ?

Answer 1

Joe is 43 years old.

Explanation:

Let x be the age of Joe Foster at present

Let y be the age of his daughter at present

Six years ago, their ages are:

x - 6 and y - 6 respectively

Six years from now, their ages will be:

x + 6 and y + 6

Six years ago, Joe Foster was two years more than five times as old as his daughter.

(x - 6) = 5(y-6) + 2

Simplify

x - 6 = 5y - 30 + 2

x = 5y -30 + 2 + 6

x = 5y - 22 ---equation 1

Six years from now, he will be 11 years more than twice as old as she will be.

(x + 6) = 2(y+6) + 11

Simplify

x + 6 = 2y + 12 + 11

x = 2y + 12 + 11 -6

x = 2y + 17 ----equation 2

Subtract equation 2 from equation 1

x = 5y - 22

-(x = 2y + 17)

0 = 3y - 39

Transpose

3y = 39

y = 39/3

y = 13

Substitute y = 3 to equation 1 x = 5y - 22

x = 5(13) - 22

x = 65 - 22

x = 43