Start off by assigning variables to each person.
Let x = Jay's age now
Let 2x = Jay's father's age now
Based on these variables for current ages, we can add 20 years to each variable to find ages in 20 years.
x + 20 will be Jay's age is 20 years
2x + 20 will be Jay's father's age in 20 years.
Now for writing the equation. Jay's age in 20 years (x+20) is 2/3 of Jay's father's age in 20 years (2x + 20). Therefore, the equation will be the following:
x + 20 = 2/3 (2x + 20)
x + 20 = (4/3)x + 40/3
20 - (40/3) = (4/3)x - x
6 2/3 = (1/3) x
x = 20 (Jay's age now)
2x = 40 (Jay's father's age now)
Checking your answer:
If Jay's age now is 20, his age in 20 years (x+20) must be 40.
If Jay's father's age now is 40, his age in 20 years (2x+20) must be 60.
Therefore, Jay's age in 20 years is 2/3 of Jay's father's age in 20 years. This fits with the facts given in the problem.
Final answer:
Jay is 20 years old now.
Jay's father is 40 years old now.
