Question

A math test is worth 100 points and has 38 problems. Each problem is worth either 5 points or 2 points. How many problems of each points value are on the test

Answer 1

Let x be the number of 5 points question.
Let y be the number of 2 points question.

Total number of questions is 38
x + y = 38 

Total points is 100
5x + 2y = 100

x + y = 38 ------------- (1)
5x + 2y = 100 ---------(2)

From (1):
x + y = 38
x = 38 - y -------------- sub into (2)
5(38 - y) + 2y = 100
190 - 5y + 2y = 100
3y = 90
y = 30 ------------------ sub into (1)
x + 30 = 38
x = 38 - 30
x = 8

There are 8 5-point questions and 30 2-point questions

Answer 2

Let x be the number of 5 points question.

Let y be the number of 2 points question.

Total number of questions is 38

x + y = 38 

Total points is 100

5x + 2y = 100

x + y = 38 ------------- (1)

5x + 2y = 100 ---------(2)

From (1):

x + y = 38

x = 38 - y -------------- sub into (2)

5(38 - y) + 2y = 100

190 - 5y + 2y = 100

3y = 90

y = 30 ------------------ sub into (1)

x + 30 = 38

x = 38 - 30

x = 8

There are 8 5-point questions and 30 2-point questions

hope this helps you