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Bravo!
Answer
:
16
correct, 10 incorrect
Let's denote the number of correct answers as \( C \) and the number of
incorrect answers as \( I \). The father pays $5.00 for each correct
answer and receives $8.00 for each incorrect answer.
The total amount the father pays is \( 5C \), and the total amount the son pays is \( 8I \).
According to the problem, no money was exchanged, so:
\[ 5C - 8I = 0 \]
Now, we know that the boy answered a total of 26 questions:
\[ C + I = 26 \]
Now, we have a system of two equations:
\[ \begin{cases} 5C - 8I = 0 \\ C + I = 26 \end{cases} \]
We can solve this system to find the values of \( C \) and \( I \).
One way to solve it is to multiply the second equation by 8 and add it to the first equation to eliminate \( I \):
\[ \begin{cases} 5C - 8I = 0 \\ 8(C + I) = 8 \times 26 \end{cases} \]
This simplifies to:
\[ \begin{cases} 5C - 8I = 0 \\ 8C + 8I = 208 \end{cases} \]
Now, add the two equations:
\[ 5C - 8I + 8C + 8I = 0 + 208 \]
Combine like terms:
\[ 13C = 208 \]
Divide by 13:
\[ C = 16 \]
Now that we know \( C \), substitute it back into the second equation to find \( I \):
\[ 16 + I = 26 \]
Subtract 16 from both sides:
\[ I = 10 \]
So, the boy got 16 correct answers and 10 incorrect answers. |
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