Math question using linear equations

Question

Alan's height is 4/5 of his father's height. Alan's older brother, Ben, is 6 cm taller than Alan. Ben's height is 5/6 of their father's height. How tall is their father?

Answer 1

Janis,

First let's identify the variables. Let a = Alan' height. Let b = Ben's height. Let f = father's height.

Since we are asked to solve for the father's height, let's express Alan's and Ben's heights in terms of father's height:

a = 4/5f (Alan is 4/5 his father's height.)

b = 5/6 f (Ben is 5/6 his father's height.)

We also know that Ben is 6 cm taller than Alan:

b = 4/5f + 6

We now have two equations that start with b =. We can set the other sides of these equations equal to each other:

4/5f + 6 = 5/6f

And solve for f:

6 = 5/6f - 4/5f

6 = 1/30f

f = 180

Father's height is 180 cm, or approximately 5 ft 9 in tall.