Question

An exam worth 148 points contains 36 questions. Some questions are worth 2 points, and the others are worth 6 points. How many 2 point and 6 point questions are on the test?

Answer 1

In order to solve for this question, let's assign a couple variables.

The variable 't' will represent the number of two-point questions, and the variable 's' will represent the number of six point questions.

From the given, we can already form two equations:

t + s = 36

("An exam... contains 36 questions")

2t + 6s = 148

("An exam worth 148 points... Some questions are worth 2 points, and the others are worth 6 points")

Before we begin calculating anything, we can simplify the second equation we made, since all the numbers are divisible by 2:

2t + 6s = 148

t + 3s = 74

Now let's refer back to the first equation. We can subtract both sides by 's' (you could also subtract both sides by 't', but I personally think that this will make solving the equation less difficult):

t + s = 36

t = 36 - s

This effectively gives us a value for the variable 't'. We can assign this value back into our first equation:

t + 3s = 74

(36 - s) + 3s = 74

36 + 2s = 74

2s = 38

s = 19

Input 's' into our second equation to solve for 't':

t = 36 - s

t = 36 - 19

t = 17

There are 17 two-point questions and 19 six-point questions

- T.B.