10 essay questions
Explanation
Step 1
Set the equations
Let x represents the number of multiple choices correct answers
Let y represents the number of essay correct answers
so
a) the total questions is 28
the total points is 134
points for correct multiple choice answer:3
points for correct essay answer:8
so
[tex]\begin{gathered} x+y=28\Rightarrow equation(1) \\ 3x+8y=134\Rightarrow equation(2) \end{gathered}[/tex]Step 2
solve the equations
[tex]\begin{gathered} x+y=28\Rightarrow equation(1) \\ 3x+8y=134\Rightarrow equation(2) \end{gathered}[/tex]a) isolate x in equation (1) and then, replace the result in equation(2)
[tex]\begin{gathered} x+y=28\Rightarrow equation(1) \\ \text{subtract y in both sides} \\ x+y-y=28-y \\ x=28-y \end{gathered}[/tex]replace in equation (2)
[tex]\begin{gathered} 3x+8y=134\Rightarrow equation(2) \\ 3(28-y)+8y=134 \\ \text{break the parenthesis} \\ 84-3y+8y=134 \\ \text{add like terms} \\ 84+5y=134 \\ \text{subtract 84 in both sides} \\ 84+5y-84=134-84 \\ 5y=50 \\ \text{divide both sides by 5} \\ \frac{5y}{5}=\frac{50}{5} \\ y=10 \end{gathered}[/tex]hence, the number of eassy question is 10
b) now, replace in equation(1) to find y
[tex]\begin{gathered} x+y=28\Rightarrow equation(1) \\ \text{replace} \\ x+10=28 \\ \text{subtract 10 in both sides} \\ x+10-10=28-10 \\ x=18 \end{gathered}[/tex]so, the number of multiple question is 18
therefore,
the answer is
10 essay questions
