A father is 4 times as old as his son. 5 years ago the sum of their age was 70. Find their present age.
son's age --- x
father's age -- 4x
5 years ago:
son's age = x-5
father's age = 4x-5
x-5 + 4x-5 = 70
solve for x, plug into my definitions
To solve this problem, let's create two equations based on the given information.
Let the son's present age be represented by S, and the father's present age be represented by F.
We are given that the father is 4 times as old as his son, so we can write the equation:
F = 4S ....(equation 1)
We are also given that 5 years ago, the sum of their ages was 70. So, 5 years ago, the son's age would have been S - 5, and the father's age would have been F - 5. The sum of their ages 5 years ago was 70, so we can write the equation:
(S - 5) + (F - 5) = 70
Now, let's substitute the value of F from equation 1 into the second equation:
(S - 5) + (4S - 5) = 70
Simplifying this equation, we have:
5S - 10 = 70
Add 10 to both sides of the equation:
5S = 80
Divide both sides of the equation by 5:
S = 16
Now, substitute the value of S into equation 1 to find the father's age:
F = 4S = 4(16) = 64
Therefore, the son's present age is 16 and the father's present age is 64.