Question

An exam worth 64 points has 13 questions. Some of the questions are worth 4 points and others are worth 7 points. How many 7 point questions and 4 point questions were on the test?

Answer 1

Let m represent the number of 4 point questions

Let n represent the number of 7 point questions

The exam has 13 questions, which means that the total number of 4 point and 7 points questions is 13, this can be represented as

m + n = 13 --------------equation (1)

The exam worth 64 points

This can be represented as

4m + 7n = 64 --------------equation (2)

solving both equations simultaneously, we have

m + n = 13 --------------equation (1)

4m + 7n = 64 --------------equation (2)

from equation (1), m= 13 - n

substitute m = 13 - n into equation (2)

4(13 - n) + 7n = 64

52 - 4n +7n =64

3n + 52 = 64

3n = 64 -52

3n = 12

n=12/3

n=4

Sunstitute n = 4 into equation(1)

m + n = 13

m + 4 = 13

m=13-4

m= 9

Hence, There are four 7 point questions