Answer:
Multiple Choice: 2 Points Each
Short Response: 4 Points Each
Step-by-step explanation:
This is a system of equations problem.
The way I solved it was by, first, organizing two equations.
m(23)+s(10)=86 and m(28)+s(5)=76
m = multiple-choice question points
s = short response question points
The first equation is your scores. m(23)+s(10)=86
You had 23 multiple choice questions and 10 short response questions. Your score on the test was 86.
The second equation is your friend's score. m(28)+s(5)=76
They had 28 multiple choice questions and 5 short response questions. They scored a 76 on the test.
Solve m(23)+s(10)=86;m(28)+s(5)=76
23m+10s=86 for m
Add -10s to both sides.
23m+10s+−10s=86+−10s
23m=−10s+86
Divide both sides by 23.
[tex]\frac{23m}{23}=\frac{-10s+86}{23}[/tex]
m=[tex]\frac{-10}{23} s+\frac{86}{23}[/tex]
Substitute [tex]\frac{-10}{23} s+\frac{86}{23}[/tex] for m in 28m+5s=76.
28m+5s=76
28( [tex]\frac{-10}{23} s+\frac{86}{23}[/tex])+5s=76
Simplify both sides of the equation.
[tex]\frac{-165}{23} s+\frac{2408}{23} =76[/tex]
Add [tex]\frac{-2408}{23}[/tex] to both sides.
[tex]\frac{-165}{23} s+\frac{2408}{23} +\frac{-2408}{23} =76+\frac{-2408}{23}[/tex]
[tex]\frac{165}{23} s=\frac{-660}{23}[/tex]
[tex]\frac{\frac{-165}{23}s}{\frac{-165}{23}}=\frac{\frac{-660}{23}}{\frac{-165}{23}}[/tex]
s=4
Substitute 4 for s in m=[tex]\frac{-10}{23}s+\frac{86}{23}[/tex]
m=[tex]\frac{-10}{23}s+\frac{86}{23}[/tex]
m=[tex]\frac{-10}{23}(4)+\frac{86}{23}[/tex]
Simplify both sides of the equation.
m=2
Answer:
m=2 and s=4
This is a lot of work. Can I please actually get brainliest?
