Question

​Greg's age is 6 less than 5 times​ Rachel's age. In four years the sum of their ages will be 20. How old is each person​ now?

Answer 1

Rachels age = 3 years

Greg's age = 9 years

Explanation:

Framing algebraic equations and solving:

Present age:

Let Rachels age = x years

5 time of Rachel's age = 5*x = 5x

6 less than 5x = 5x - 6

Greg's age = (5x - 6) years

Age after four years:

Rachel's age = (x + 4) years

Greg's age = 5x - 6 + 4

= ( 5x - 2) years

Sum of their ages = 20

x + 4 + 5x - 2 = 20

x + 5x + 4 - 2 = 20

Combine like terms,

6x + 2 = 20

Subtract 2 from both sides,

6x = 20 - 2

6x = 18

Divide both sides by 6,

x = 18 ÷ 6

x = 3

Rachel's age = 3 years

Greg's age = 5*3 - 6

= 15 - 6

= 9 years