SOLUTION: The ages of two brothers are in the ratio two to three, but in eight years, the ratio of their ages will be three to four. What is the age of the older brother?

Question 435314: The ages of two brothers are in the ratio two to three, but in eight years, the ratio of their ages will be three to four. What is the age of the older brother?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The ages of two brothers are in the ratio two to three, but in eight years, the ratio of their ages will be three to four. What is the age of the older brother?
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Let the brothers be a and b.
Equations:
a/b = 2/3
(a+8)/(b+8) = 3/4
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Cross multiply:
3a = 2b
4(a+8) = 3(b+8)
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a = (2/3)b
4a+32 = 3b+24
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substitute for "a" and solve for "b":
4(2/3)b + 32 = 3b+24
[(8/3)-(9/3)]b = -8
(-1/3]b = -8
b = 24 years old
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a = (2/3)b
a = (2/3)24
a = 16 years old
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Cheers,
Stan H.
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