Question

A test is worth 100 points. The test is made up of 40 items. Each item is worth either 2 points or 3 points. Which matrix equation and solution represent the situation?

Answer 1

C

Explanation:

Got 100% on edge

[1 1 40]

[2 3 100]

There are 20 items worth 2 points each and 20 items worth 3 points each.

Answer 2

Total number of points in the test = 100

Total number of items in the test = 40

Let number of items of 2 points be x and number of items of 3 points be y.

Now, using the given information the situation can be represented by using the following equations :

⇒ x + y = 40 .........(1)

⇒ 2x + 3y = 100 .........(2)

The matrix equation is :

`\begin{bmatrix}1 & 1\\ 2& 3\end{bmatrix}\cdot \begin{bmatrix}x\\ y\end{bmatrix}=\begin{bmatrix}40\\ 100\end{bmatrix}`

By solving the equation (1) and equation (2), we get :

Solution : x = 20 and y = 20