Answer: Jhon is 42 years old, and his son is 21 years old.
Explanation:
Let's define:
J = John's age
S = Age of the son.
We know that:
"John is twice as old as his son"
J = 2*S
"In 42 years, the ratio of their ages will be 4:3. What is the son's current age?"
In 42, their ages will be:
J + 42 and S + 42.
And the ratio 4:3 means that:
(J + 42) = (4/3)*(S + 42)
Then we have the system of equations:
J = 2*S
(J + 42) = (4/3)*(S + 42)
To solve it we can first replace the first equation into the second one, to get:
(2*S + 42) = (4/3)*(S + 42)
2*S - (4/3)*S = (4/3)*42 - 42
S*(6/3 - 4/3) = (1/3)*42
S*(2/3) = (1/3)*42
S = (3/2)*(1/3)*42 = 21.
And we can find Jonh's age if we use the first equation:
J = 2*S = 2*21 = 42
Jhon is 42 years old, and his son is 21 years old.