2. A boy and his father played 26 games of checkers. For every game the boy lost, he gave his father 5 cents. For every game the

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2. A boy and his father played 26 games of checkers. For every game the boy lost, he gave his father 5 cents. For every game the

boy won, his father gave him 8 cents. When all the games were played, neither had won nor lost anything. The number of games the boy won i

Mathematics

1 answer:

zzz [12.3K] · Answer 1 · 2026-03-23T02:23:26+03:00

Answer: the boy won 10 games

Step-by-step explanation:

Let's denote B for the games won by the boy, and F for the games the father won.

We know that there are a total of 26 games:

B + F = 26.

For each game the boy wins, he gains 8 cents, while for each game lost to his father, he loses 5 cents. Since at the conclusion of the 26 games his total earnings net to zero, we have:

B*8 + F*(-5) = 0.

Now we form a system of equations:

B + F = 26

8*B - 5*F = 0.

Our first move is to isolate one variable. We'll start by expressing F in terms of B using the first equation:

B + F = 26

F = 26 - B.

Now substituting this into the second equation gives us:

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

Thus, the boy emerged victorious in 10 games (the father won the remaining 16 games).