Fraction word problem

Question

Alex's age now is 6/7 that of Kate's. Eight years ago, Alex's age was 2/7 as much as Kate's present age. Kate is now k years old. What is the value of k?

Answer 1

Let's set up some equations, using the initials as variables.

A = 6/7 K. Alex's age is 6/7 Kate's age

A-8 = 2/7K. Eight years ago, Alex's age was 2/7 as much as Kate's present age.

Let's use substitution, since A = 6/7 K we can substitute 6/7 K for A in the 2nd equation

6/7 K - 8 = 2/7 K

subtract 6/7 K from both sides

-8 = -4/7 K

multiply both sides by 7

-56 = -4K

Divide both sides by -4

14 = K

Kate is now 14 years old.