Answer:
option C is correct.
12 multiple-choice questions are on the test
Step-by-step explanation:
Given: The system of equation :
m + f = 15 ......[1]
3m + 5f =51 .......[2]
where m is the number of multiple choice questions and f is the number of free response questions.
Now, multiply 3 to both sides of an equation in [1];
[tex]3 \cdot (m+f) = 3\cdot 15[/tex]
Simplify:
3m + 3f = 45
Now, subtract 3f to both sides of an equation:
3m + 3f -3f = 45 -3f
Simplify:
3m = 45 -3f ......[3]
Substitute the equation [3] in [2];
45 -3f +5f = 51
Combine like terms;
45 + 2f = 51
Subtract 45 to both sides of an equation we get;
45+ 2f -45 =51-45
Simplify:
2f = 6
Divide by 2 to both sides of an equation:
[tex]\frac{2f}{2} =\frac{6}{2}[/tex]
Simplify:
f = 3
Substitute the value of f = 3 in equation [1] solve for m;
m + 3 = 15
Subtracting 3 from both sides we get
m + 3 -3 = 15 - 3
Simplify:
m = 12
Therefore, the number of multiple-choice questions are on the test is; 12
