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?

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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) About Me  (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.