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On a television game show, contestants earn 5 points for each correct answer but lose 2 points for each wrong answer. On last week's show, the winning contestant earned 80 points and answered 30 questions.

Given that [tex]$x$[/tex] represents the number of questions answered correctly, and [tex]$y$[/tex] represents the number of questions answered incorrectly, determine which system of equations correctly represents this situation.

A.
[tex]\[
\begin{array}{r}
5x - 2y = 30 \\
x + y = 80
\end{array}
\][/tex]

B.
[tex]\[
\begin{array}{r}
5x + 2y = 30 \\
x - y = 80
\end{array}
\][/tex]

C.
[tex]\[
\begin{array}{r}
5x - 2y = 80 \\
x + y = 30
\end{array}
\][/tex]

D.
[tex]\[
\begin{array}{r}
5x + 2y = 80 \\
x - y = 30
\end{array}
\][/tex]

Sagot :

GinnyAnsweridn
Let's determine the correct system of equations based on the information given in the problem.

Let's denote:
- [tex]\( x \)[/tex] as the number of questions answered correctly.
- [tex]\( y \)[/tex] as the number of questions answered incorrectly.

We need to set up two equations based on the problem's conditions:

1. Points Condition:
- Each correct answer gives 5 points.
- Each incorrect answer deducts 2 points.
- The total points earned by the contestant is 80.

So, the equation reflecting the points condition is:
[tex]\[ 5x - 2y = 80 \][/tex]

2. Total Questions Condition:
- The contestant answered a total of 30 questions.

So, the equation reflecting the total number of questions is:
[tex]\[ x + y = 30 \][/tex]

Thus, the system of equations that correctly represents the situation is:
[tex]\[ \begin{array}{r} 5x - 2y = 80 \\ x + y = 30 \end{array} \][/tex]

Notice that this matches the following system provided in the options:
[tex]\[ \begin{array}{r} 5x - 2y = 80 \\ x + y = 30 \end{array} \][/tex]

So, the correct system of equations is:
[tex]\[ \begin{array}{r} 5 x - 2 y = 80 \\ x + y = 30 \end{array} \][/tex]
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