Answer: the boy won 10 games
Step-by-step explanation:
Let's call B as the number of games won by the boy, and F as the number of games won by the father.
We know that, there is a total of 26 games:
B + F = 26.
We know that in each game won by the boy, he wins 8 cents, for every game that the father wins, the boy losses 5 cents, and we know that at the end of the 26 games, the boy did not win or lose any money, so we have:
B*8 + F*(-5) = 0.
Then we have a system of equations:
B + F = 26
8*B - 5*F = 0.
The first step is isolating one of the variables. Let's start isolating F in the first equation:
B + F = 26
F = 26 - B.
Now we can replace this in the second equation:
8*B - 5*F = 0
8*B - 5*(26 - B) = 0
8*B + 5*B - 5*26 = 0
13*B = 5*26
B = 5*26/13 = 5*2 = 10
So the boy won 10 games (then the father won the other 16 games)
