The ratio of the current ages of a mother and her son is 6:1. Five years from now, the corresponding ratio of the ages will be 7:2. What was the mother's age when her son was born?
Question
The ratio of the current ages of a mother and her son is 6:1. Five years from now, the corresponding ratio of the ages will be 7:2. What was the mother's age when her son was born?
Solution
Let's denote the current age of the mother as 6x and the current age of the son as x.
Five years from now, the mother will be 6x + 5 years old and the son will be x + 5 years old. According to the problem, the ratio of their ages at that time will be 7:2.
So, we can set up the equation:
(6x + 5) / (x + 5) = 7 / 2
Solving this equation will give us the value of x, which represents the current age of the son.
After finding x, we can find the mother's age when the son was born by subtracting the son's current age from the mother's current age.
Let's solve the equation:
Cross multiply to get rid of the fraction:
2*(6x + 5) = 7*(x + 5)
Expand both sides:
12x + 10 = 7x + 35
Subtract 7x from both sides:
5x = 25
Divide by 5:
x = 5
So, the son is currently 5 years old and the mother is currently 6*5 = 30 years old.
Therefore, the mother's age when the son was born is 30 - 5 = 25 years old.
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