SOLUTION: Sophia’s math test is worth 130 points and has 40 problems. Each problem is worth either 4 points or 3 points. How many of each question type were on the test?
A. The test had 3
Algebra ->
Average
-> SOLUTION: Sophia’s math test is worth 130 points and has 40 problems. Each problem is worth either 4 points or 3 points. How many of each question type were on the test?
A. The test had 3
Log On
Question 1017360: Sophia’s math test is worth 130 points and has 40 problems. Each problem is worth either 4 points or 3 points. How many of each question type were on the test?
A. The test had 30 4-point questions and 10 3-point questions.
B. The test had 10 4-point questions and 30 3-point questions.
C. The test had 28 4-point questions and 12 3-point questions.
D. The test had 25 4-point questions and 10 3-point questions.
First I used process of elimination and figured out that A and C were wrong. This is because it doesn't add up to the total 130.
then I wrote out the equation in numbers
4x+3y=130
X+Y=40
now this is where I got stuck.
Any help is appreciated!
Thanks Answer by macston(5194) (Show Source):
You can put this solution on YOUR website! .
USING SUBSTITUTION:
.
T=number of three point questions; F=number of four pint question
.
T+F=40
T=40-F . Use this to substitute for T below.
.
3T+4F=130 . Substitute for T from above.
3(40-F)+4F=130
120-3F+4F=130
F=10
.
T=40-F=40-10=30
.
ANSWER: There were thirty 3 point and ten 4 point questions.
.
CHECK:
3T+4F=130
3(30)+4(10)=130
90+40=130
.
-OR-
.
USING ELIMINATION:
.
3T+4F=130
.
T+F=40 . Multiply by 3.
3T+3F=120 . Subtract from first equation.
.
.(3T+4F=130)
-(3T+3F=120)
--------------
F=10
.
Same as above.
.
