Question

Janice wants to create a test containing 20 Questions worth 50 points. If Janice creates questions worth either two points or four points, she can include _____2-point questions and ____ four-point questions

Answer 1

The test question shall contain 20 questions in all.

Therefore, if the 2-point question is x, and the 4-point question is y then

x + y = 20

Also, all the 2-point questions plus all the 4-point questions all added together would equal 50points. Therefore, that would be

2x + 4y = 50

With these pair of simultaneous equations we can now solve as follows;

`\begin{gathered} x+y=20---(1) \\ 2x+4y=50---(2) \\ \text{Make x=20-y in equation (1)} \\ \text{Substitute for the value of x into equation (2)} \\ 2(20-y)+4y=50 \\ 40-2y+4y=50 \\ \text{Collect all like terms} \\ 4y-2y=50-40 \\ 2y=10 \\ \text{Divide both sides by 2} \\ y=5 \\ \text{Substitute for the value of y into equation (1)} \\ x+y=20 \\ x+5=20 \\ \text{Subtract 5 from both sides} \\ x=15 \end{gathered}`

Therefore, Janice can include

15 two-point test