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in a game a player starts with 100 points each question has two parts and a incorrect answer for both parts result in a loss of one point the student loses one half of a point for getting only one part of the question correct at the end of 25 question round the player has 82.5 points what to equations and solutions represent X Missed points

Respuesta :

Answer:

10 questions with an incorrect answer for both parts

15 questions with a correct answer in only one part

Explanation:

Let's call x the number of questions with an incorrect answer for both parts and y the number of questions with only one part of the question correct.

So, the equation that gives us the number of points after 25 rounds is:

100 - x - 0.5y = 82.5

Where: x + y = 25

So, solving for y, we get:

y = 25 - x

Replacing this on the initial equation and solving for x, we get:

[tex]\begin{gathered} 100-x-0.5y=82.5 \\ 100-x-0.5(25-x)=82.5 \\ 100-x-12.5+0.5x=82.5 \\ 87.5-0.5x=82.5 \\ 87.5-82.5=0.5x \\ 5=0.5x \\ \frac{5}{0.5}=x \\ 10=x \end{gathered}[/tex]

Then, the value of y is:

[tex]\begin{gathered} y=25-x \\ y=25-10 \\ y=15 \end{gathered}[/tex]

Therefore, the player gets 10 questions with an incorrect answer for both parts and 15 questions with a correct answer in only one part.

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