Question 48106: Billy is twice as old as his son. In 10 years, the ratio of their ages will be 3:5. Find their present ages. Answer by mbarugel(146) (Show Source):
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The main difficulty in age problems is to "translate" the problem into math equations.
First of all, let's define the variables B for Billy's age and S for his son's age. We're told that "Billy is twice as old as his son". This means that:
Next, we're told that "In 10 years, the ratio of their ages will be 3:5". First of all, in 10 years, Billy's age will be B + 10, and his son's age will be S + 10. We're told that the ratio between these ages is 3:5. Therefore, we get the equation:
So now you have a simple system with two equations and two unknowns:
You can solve this system with your preferred method (such as substitution). The solution is that Billy's 40 years old and his son is 20.
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