A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation. x y = 24 3x 5y = 100 What does the solution of this system indicate about the questions on the test?
A. The test contains 4 three-point questions and 20 five-point questions.

B. The test contains 10 three-point questions and 14 five-point questions.

C. The test contains 14 three-point questions and 10 five-point questions.

D. The test contains 20 three-point questions and 8 five-point questions.

Question

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msm555 msm555 · Answer 1 · 2024-02-06T02:47:16+01:00

Answer:

B: The test contains 10 three-point questions and 14 five-point questions

Step-by-step explanation:

To solve the system of equations:

[tex]\begin{cases}x + y = 24 \\3x + 5y = 100\end{cases}[/tex]

We can use the method of substitution or elimination.

Let's use the substitution method. From the first equation, we can solve for [tex]x[/tex] to get:

[tex]x = 24 - y[/tex]

Now, substitute [tex]x[/tex] into the second equation:

[tex]3(24 - y) + 5y = 100[/tex]

[tex]72 - 3y + 5y = 100[/tex]

[tex]72 + 2y = 100[/tex]

[tex]2y = 100 - 72[/tex]

[tex]2y = 28[/tex]

[tex] y =\dfrac{28}{2}[/tex]

[tex]y = 14[/tex]

Now that we have found [tex]y[/tex], we can substitute it back into the first equation to find [tex]x[/tex]:

[tex]x = 24 - 14[/tex]

[tex]x = 10[/tex]

So, the solution is [tex]x = 10[/tex] and [tex]y = 14[/tex].

This indicates that there are 10 three-point questions and 14 five-point questions on the test.

Therefore, the correct answer is option B: The test contains 10 three-point questions and 14 five-point questions.