SOLUTION: A's age is two years less than three times that of B. Eight years ago the sum of their ages was 42. How old is A?

Question 668766: A's age is two years less than three times that of B. Eight years ago the sum of their ages was 42. How old is A?
Answer by amazingrace333(11) (Show Source): You can put this solution on YOUR website!
So we know that A's age = 3 times B's age - 2 years or
A = 3B - 2
and
A's age minus 8 yrs + B's age minus 8 yrs = 42 or
A-8 + B-8 = 42
Simplify and solve for only one variable:
A + (-8) + B + (-8) = 42
Combine likes:
A + B + (-16) = 42
Simplify:
A + B = 42 + 16
A + B = 58
A = 58 - B
Substitute 58-B for A in our original equation and solve:
58-B = 3B-2
58 - B + 2 = 3B - 2 + 2
60 - B = 3B
60 -B +B = 3B + B
60 = 4B
60/4 = 4B/4
15 = B
Therefore, A = 58 - 15 or 43
Check your answer:
A's age of 43 = 3 x B's age -2 yrs or 3(15)-2 or 45-2 which is 43
So, A is 43 years old and B is 15 years old.
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