Question

A test has a total of twenty questions. The test is worth 100 points. It consists of true/false questions worth 3points each and multiple choice questions worth 11 points each. How many of each type of question are onthe test?Write and solve a system of equations to answer the question.Show your work here:Answer:There aretrue/false questions andmultiple choicequestions

Answer 1

For this problem, we were informed that a test consists of two types of questions, true/false (x) and multiple-choice (y). The test is worth 100 points, the true/false questions are worth 3 points and the multiple-choice questions are worth 11 points each. The problem also states that there are 20 questions in total. We need to determine how many questions of each type there are.

The first step we need to take in order to solve this problem is to sum the number of each type of question, the result should be equal to the number of questions in total. So we have:

`x+y=20`

If we multiply the number of points each type of question is worth by the number of questions on the test, we should have a result that is equal to the total number of points.

`3\cdot x+11\cdot y=100`

Now we have two equations, and we can create a system, such as below:

`\begin{cases}x+y=20 \\ 3\cdot x+11\cdot y=100\end{cases}`

By multiplying the first equation by -3, and adding both equations, we can eliminate one variable and solve for y.

`\begin{gathered} \begin{cases}-3x+-3y=-60 \\ 3\cdot x+11\cdot y=100\end{cases} \\ -3y+11y=-60+100 \\ 8y=40 \\ y=(40)/(8)=5 \end{gathered}`

We can now replace the value of "y" on the first equation to determine "x".

`\begin{gathered} x+5=20 \\ x=20-5 \\ x=15 \end{gathered}`

There are 15 true/false questions and 5 multiple-choice questions.