SOLUTION: A test consists of only true/false questions and multiple-choice questions. The true/false questions are worth 2 points each, and multiple-choice questions are worth 6 points each.

Algebra ->  Test -> SOLUTION: A test consists of only true/false questions and multiple-choice questions. The true/false questions are worth 2 points each, and multiple-choice questions are worth 6 points each.      Log On


   

Question 1176111: A test consists of only true/false questions and multiple-choice questions. The true/false questions are worth 2 points each, and multiple-choice questions are worth 6 points each. The test contains 20 questions and is worth a total of 100 points.
Set up a system of equations and find the solution to complete the following sentence: "There are ____ true/false questions and ____ multiple-choice questions".
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
let’s true/false questions be t and multiple-choice questions m
if the test contains 20 questions, we have
t%2Bm=20............solve for t
t=20-m...........eq.1

if the true/false questions are worth 2 points each, and multiple-choice questions are worth 6 points each, then we have
the true/false questions are worth 2tpoints
multiple-choice questions are worth 6m points

and if it is worth a total of 100 points, we have

2t%2B6m=100...........eq.2 ..........substitute t from eq.1
2%2820-m%29%2B6m=100........solve for m
40-2m%2B6m=100
4m=100-40
4m=60
m=60%2F4
m=15

go to

t=20-m...........eq.1.......substitute m
t=20-15
t=5

so, there are 5 true/false questions and 15 multiple-choice questions