The social studies teacher is giving a test worth 80 points, and containing 34 questions. There are 2 point and 4 point questions on the test. How many of each type of question are on the test

Answer 1

To solve this problem, you have to solve for 2 variables (number of 2 point questions and number of 4 point questions). So, the best way to approach it is a system of equations.

Lets call X 2 point questions and Y 4 point questions.

There are 34 questions so X+Y=34

There are 80 total points so 2X + 4Y= 80 (basically, 2 times the number of 2 point questions plus 4 times the number of 4 point questions makes up the total number of points.

So, with those two equations, let's solve.

X+Y= 34

2X+4Y=80

This equation looks easiest to do by elimination, so lets multiply the entire first equation by 2 so the Xs cancel

2(X+Y=34) comes to

2X + 2Y= 68

Now, subtract this from the other equation to solve

2X+4y=80 - (2X+2Y= 68)

2y= 12

y=6

There are 6 4 point questions.

Now, lets solve for 2 point questions by plugging into the original equation, choosing the easier one.

X + 6=34

X= 28, there are 28 2 point questions.

You should then quickly make sure your numbers work in the original equation

2X+4y=80

2(28) + 4(6)=80

56 + 24= 80

80=80

It checks out :) .

That's it!