1. The sum of ages of father and son is 64 years. Father says to son, “I am 5 times as old as you were when I was of your age.” What is the sum of digits of son’s age?
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To solve this problem, let's assume the son's age is x years.
The sum of ages of the father and son is 64 years, so the father's age is 64 - x.
According to the father's statement, he is 5 times as old as the son was when the father was of the son's current age. This can be written as:
64 - x = 5 * (x - (64 - x))
Simplifying the equation:
64 - x = 5 * (2x - 64)
64 - x = 10x - 5*64
64 - x = 10x - 320
Rearranging the equation:
11x = 256
Dividing both sides of the equation by 11:
x = 23.27
Since the age cannot be a fraction, we can assume the son's age is 23 years.
Now, to find the sum of digits of the son's age, we can simply add the digits together:
2 + 3 = 5
Therefore, the sum of digits of the son's age is 5.