help me please

Question

your teacher is giving you a test worth 100 points containing 40 questions. there are two point and for point questions on the test. how many of each type of question are on the test

Answer 1

So to write a system we need two variables.  Usually x and y, but you can use other letters if you want.

 

Lets say x = the number of 2 point questions

and y = the number of 4 point questions

 

since there are 40 questions total x + y = 40 is our first equation.

 

since there are 100 points total 2x + 4y = 100 is our second equation (these can take some getting used to writing)

 

now there's a few ways to solve these, but this one's not bad to do with either substitution or elimination.  Let's go with substitution.

 

since x + y = 40, we can solve for x and say that x = 40 - y

 

now plugging this into our second equation we get 

 

2(40 - y) + 4y = 100     distribute

80 - 2y + 4y = 100       combine like terms

80 + 2y = 100               subtract 80 on both sides

2y = 20                         divide by 2

y = 10, so there are 10 four-point questions

 

now since x + y = 40, x + 10 = 40, and x = 30.

 

Checking to make sure:

 

30 two-point questions would be 60 points.

10 four-point questions would be 40 points.

100 points total sounds good.