SOLUTION: Your science test is worth 100 points and contains 38 questions.there are two-point and five point questions on the test.How many of each type of question are on the test?

Algebra ->  Linear-equations -> SOLUTION: Your science test is worth 100 points and contains 38 questions.there are two-point and five point questions on the test.How many of each type of question are on the test?      Log On


   

Question 174906: Your science test is worth 100 points and contains 38 questions.there are two-point and five point questions on the test.How many of each type of question are on the test?
Answer by actuary(112) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the number of 2-point questions
Let y = the number of 5 point questions
x + y = 38 (There are 38 total questions)(Equation #1)
x*2 + y*5 = 100 (The total number of points is 100) (Equation #2)
Equation #1 can be rewritten as y = 38-x
This can be used to replace "y" in equation #2
So 2*x + 5*(38-x)=100
So 2*x+190-5*x=100
Therefore -3*x=100-190=-90
Solve -3*x = -90 for x by dividing each side of the equation by 3, x = 30
Since x = 30, y = 38-30 = 8 (Using equation #1)
I hope that this helps.