Respuesta :
26.67
Explanation
Step 1
let´s find the equations to solve:
a ratio is a relationship between two quantities, normally expressed as the quotient
so
[tex]\begin{gathered} \text{ratio correct answer to incorrect answer} \\ r=\frac{correct\text{ answer}}{\text{ Incorrect answer}} \end{gathered}[/tex]we are told that the raio for lesly was 8, hence
[tex]\begin{gathered} r=\frac{correct\text{ answer}}{\text{ Incorrect answer}} \\ \text{replace} \\ 8=\frac{correct\text{ answer}}{\text{ Incorrect answer}} \end{gathered}[/tex]a)
if we let
number of correct answers = x
number of incorrect answers = y
we would have
[tex]\begin{gathered} 8=\frac{correct}{In\text{correct}}=\frac{x}{y} \\ 8=\frac{x}{y}\rightarrow equation(1) \end{gathered}[/tex]b) if the total of question is 30,then
total questions= total anwers= correct answer +incorrect answer
replace
[tex]30=x+y\rightarrow equation(2)[/tex]Step 2
solve the equations
a) isolate the x value from equation (2) and replace in equation (1)
[tex]\begin{gathered} 30=x+y \\ \text{subtract y in both sides} \\ 30-y=x+y-y \\ 30-y=x \end{gathered}[/tex]replace the x value in equation(1)
[tex]\begin{gathered} 8=\frac{x}{y}\rightarrow equation(1) \\ 8=\frac{30-y}{y} \\ \text{cross multiply} \\ 8y=30-y \\ 8y+y=30 \\ \text{9y}=30 \\ y=\frac{30}{9} \\ y=\frac{10}{3} \\ \\ \end{gathered}[/tex]replace the y value in equation (2)
[tex]\begin{gathered} 30=x+y\rightarrow equation(2) \\ 30=x+\frac{10}{3} \\ \text{subtract 10/3in both sides} \\ 30-\frac{10}{3}=x+\frac{10}{3}-\frac{10}{3} \\ \frac{80}{3}=x \end{gathered}[/tex]so, the total of correct answer is x
x=80/3= 26.67
the numbers of correct answer is 26.67
I hope this helps you
