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How Might You Win?

By analyzing past episodes of the quiz show, you realize that you will probably need 600 points to defeat Kimberly.

You also notice that, on average, you only feel confident enough to respond to 12 of the 20 questions on a typical episode.

If you respond to only 12 questions when you're on the show, which two equations describe your winning scenario? Select all the correct answers.

[tex]100x - 200y = 600[/tex]
[tex]x + y = 600[/tex]
[tex]100x - 200y = 12[/tex]
[tex]x - y = 600[/tex]
[tex]x + y = 12[/tex]



Answer :

GinnyAnswer
Let's dive into the problem and derive the two equations that describe your winning scenario:

1. We are given that you feel confident to respond to only 12 questions. We can denote the number of questions you feel confident to answer correctly as [tex]\( x \)[/tex] and the number of questions you do not feel confident about as [tex]\( y \)[/tex].

Since you respond to a total of 12 questions, the first equation can be written as:
[tex]\[ x + y = 12 \][/tex]

2. You need 600 points to defeat Kimberly. Let's assume each correct response earns you 100 points, and each incorrect response loses you 200 points.

From this, the total points you can earn can be expressed as a function of the number of correct and incorrect responses:
[tex]\[ 100x - 200y = 600 \][/tex]

These two equations represent your winning scenario:

1. [tex]\( x + y = 12 \)[/tex]
2. [tex]\( 100 x - 200 y = 600 \)[/tex]

Hence, the correct equations are:
[tex]\[ \boxed{x + y = 12} \][/tex]
[tex]\[ \boxed{100 x - 200 y = 600} \][/tex]

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