Answered

Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Get quick and reliable solutions to your questions from a community of experienced professionals on our platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

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.
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.