back to Algebra 1 video lessons

How to translate word sentence into algebra expression and write one variable equation?

Question:

This year the father's age is three times that of his son. Seven years ago, the father's age was four less than five times the son's age. How old are father and son this year?

Solution:

Let x be the son's age in this year.
This year the fater's age is 3x
Seven years ago, the son's age is x - 7
Seven years ago, the father's age is 3x - 7
relationship: seven years ago, the father's age was four less than five times the son's age.
3x - 7 = 5 (x - 7) - 4
3x - 7 = 5x - 35 - 4
3x - 7 = 5x - 39
5x - 3x = 39 - 7
2x = 32
x = 16
3x = 3 × 16 = 48

This year the son is 16 year old and the father is 48 years old.