SOLUTION: The ages of three brothers are consecutive even intergers. Three time the age of the youngest brother exceeds the oldest brother's age by 48 years. What is the age of the youngest

Question 527787: The ages of three brothers are consecutive even intergers. Three time the age of the youngest brother exceeds the oldest brother's age by 48 years. What is the age of the youngest brother?
Answer by lmeeks54(111) (Show Source): You can put this solution on YOUR website!
Let a = age of oldest brother today
Let b = age of middle brother today
Let c = age of youngest brother today
...
The ages are consecutive even integers means:
a = b + 2
a = c + 4
...
though it seems like we have 3 unknowns, which would require at least three equations to solve it, because of the relationship between a, b, and c (e.g., a = c + 4), we can consider this a system of two equations with two unknowns:
...
3c = a + 48
a = c + 4
...
if we substitute a from the 2nd equation into the first, we have one equation with one unknown, which is easily solved:
...
3c = (c + 4) + 48, which simplifies to:
3c = c + 52
...
By subtracting c from both sides, we have:
2c = 52, or:
c = 26
...
Going back to our original relationships, we recall:
a = c + 4
b = c + 2
...
so substituting c = 26 into both equations, we have:
...
a = 30, b = 28, c = 26
...
checking our work:
3(26) = (30) + 48
78 = 78 checks
...
cheers,
Lee
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