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?
mc008-1.jpg
There are 20 items worth 2 points each and 20 items worth 3 points each.

mc008-2.jpg
There are 10 items worth 2 points each and 30 items worth 3 points each.

mc008-3.jpg
There are 20 items worth 2 points each and 20 items worth 3 points each.

mc008-4.jpg
There are 10 items worth 2 points each and 30 items worth 3 points each.

Answer 1

Let x = number of 2‑point items and y = number of 3‑point items. The system is
x + y = 40
2x + 3y = 100

In matrix form:
[ [1 1]
[2 3] ] [x
y] = [40
100]

Solve: from x + y = 40, y = 40 − x. Substitute: 2x + 3(40 − x) = 100 → −x + 120 = 100 → x = 20, y = 20.

So there are 20 two‑point items and 20 three‑point items (matrix as above, solution [20;20]).