Answered

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What is a system of equations for the following situation?

There is a total of 30 questions on a test. Some questions are multiple-choice and some are short answer. The multiple-choice questions are worth 2 points and the short answer questions are worth 6 points. There is a total of 100 points on the test.

[tex]\[
\begin{array}{l}
\left\{
\begin{array}{l}
m + s = 30 \\
2m + 6s = 100
\end{array}
\right.
\end{array}
\][/tex]

Sagot :

GinnyAnswer
To determine the system of equations for the given situation, let's break down the problem step-by-step.

1. Define the variables:
- Let [tex]\( m \)[/tex] be the number of multiple-choice questions.
- Let [tex]\( s \)[/tex] be the number of short answer questions.

2. Translate the word problem into mathematical equations.

First, we know the total number of questions on the test:

[tex]\[ m + s = 30 \][/tex]

Second, we know the total number of points on the test. Multiple-choice questions are worth 2 points each, and short answer questions are worth 6 points each. The total points accumulated from both types of questions must sum up to 100:

[tex]\[ 2m + 6s = 100 \][/tex]

Hence, the correct system of equations to represent the situation is:

[tex]\[ \begin{cases} m + s = 30 \\ 2m + 6s = 100 \end{cases} \][/tex]

This system accurately models the given scenario. It tells us that the sum of multiple-choice and short answer questions is 30, and the total points from these questions sum to 100.
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