the ages of a son and father are in ratio 3:8. If the son is 35 years younger than his father find their ages.
8x-280=3x
8x-3x=280
5x=280
x=56
x = father's age
x - 35 = son's age
3/8 = (x - 35)/x
cross multiply
8(x - 35) = 3x
To find the ages of the son and the father, we can set up a system of equations based on the given information.
Let's assume the son's age is represented by 3x, where x is a multiplier. Since the ratio of the son's age to the father's age is 3:8, we can deduce that the father's age is 8x.
According to the information given, the son is 35 years younger than the father. Therefore, we have the equation:
8x - 35 = 3x
To solve this equation, we can combine like terms:
8x - 3x = 35
Simplifying further:
5x = 35
To isolate x, we divide both sides of the equation by 5:
x = 7
Now that we have the value of x, we can substitute it back into the expressions for the son and father's ages.
Son's age = 3x = 3 * 7 = 21 years
Father's age = 8x = 8 * 7 = 56 years
Therefore, the son is 21 years old, and the father is 56 years old.