Question 1105083
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.