I need help please

Question

a teacher is giving you a 120 point test containing 40 question. There are two point and four point questions on the test. How many type of question are on the test? 

Answer 1

Say a = # of 2-point questions, and b = # of 4-point questions. That means a+b = 40 questions.

We also know that there are 120 total points. Therefore --> 120 = 2a + 4b (multiplying 2 times a gives us the total points on 2-point questions, and 4 times b gives us the total points on 4-point questions). 

 

If we rearrange the first equation, we get b = 40-a, and we can plug this into the second equation to solve for a. 

120 = 2a + 4(40-a)

120 = 2a + 160 - 4a

-40 = -2a

a = 20

 

Plugging a back into the original equation shows that there must be 20 2-point questions (a) and 20 4-point questions (b). 

Answer 2

Let x be the number of 4 point questions, so number of 2 point questions is 40 - x:

 

120 = 4x + 2(40 - x)

 

120 = 4x + 80 - 2x

 

120 = 2x + 80

 

120 - 80 = 2x

 

40 = 2x

 

x = 20

 

there are 20 4 point and 20 2 point questions.

 

Answer 3

Let x = the number of 2-point questions and y = the number of 4-point questions.

 

Then

 

x + y = 40

 

2x + 4y = 120

 

 

Solve for y in the first equation to substitute into the second equation.

 

y = 40 - x

 

2x + 4(40 - x) = 120

 

 

Solving for x:

 

2x + 160 - 4x = 120

 

-2x = -40

 

x = 20

 

 

So, y = 20 and there are 20 questions of each type on the exam.