Question 1105083: Sam’s younger brother was half Sam’s age when Sam was half the age of his older brother. 7 years later, Sam’s younger brother was 2/3 Sam’s age and 2/5 the age of Sam’s older brother. How old is Sam now?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! A = sam's younger brother's age now.
B = sam's age now.
C = sam's older brother's age now.
A = 1/2 * B
B = 1/2 * C
A + 7 = 2/3 * (B + 7)
A + 7 = 2/5 * (C + 7)
replace A with 1/2 * B in the equation of A + 7 = 2/3 * (B + 7).
you will get 1/2 * B + 7 = 2/3 * (B + 7).
simplify to get 1/2 * B + 7 = 2/3 * B + 2/3 * 7.
multiply both sides of this equation by 6 to get 3 * B + 42 = 4 * B + 28.
subtract 3 * B from both sides of this equation and subtract 28 from both sides of this equation to get 42 - 28 = 4 * B - 3 * B.
combine like terms to get 14 = B.
since A = 1/2 * B, then A = 7
since B = 1/2 * C, then C = 28
you have:
A = 7
B = 14
C = 28
you also have:
A + 7 = 14
B + 7 = 21
C + 7 = 35
A = 1/2 * B becomes 7 = 1/2 * 14 which is true.
B = 1/2 * C becomes 14 = 1/2 * 28 which is true.
A + 7 = 2/3 * (B + 7) becomes 14 = 1/3 * 21 which is true.
A + 7 = 2/5 * (C + 7) becomes 14 = 2/5 * 35 which is true.
the solution is confirmed to be good.
since B = sam's age now, the solution is that sam's age now is 14.
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