Question

8. Lesly took a test with 30 questions. The ratio of correct answers to incorrect answersfor Lesly Was to 8. How many answers did she get correct?

Answer 1

26.67

Step-by-step explanation

Step 1

let´s find the equations to solve:

a ratio is a relationship between two quantities, normally expressed as the quotient

so

`\begin{gathered} \text{ratio correct answer to incorrect answer} \\ r=\frac{correct\text{ answer}}{\text{ Incorrect answer}} \end{gathered}`

we are told that the raio for lesly was 8, hence

`\begin{gathered} r=\frac{correct\text{ answer}}{\text{ Incorrect answer}} \\ \text{replace} \\ 8=\frac{correct\text{ answer}}{\text{ Incorrect answer}} \end{gathered}`

a)

if we let

number of correct answers = x

number of incorrect answers = y

we would have

`\begin{gathered} 8=\frac{correct}{In\text{correct}}=(x)/(y) \\ 8=(x)/(y)\rightarrow equation(1) \end{gathered}`

b) if the total of question is 30,then

total questions= total anwers= correct answer +incorrect answer

replace

`30=x+y\rightarrow equation(2)`

Step 2

solve the equations

a) isolate the x value from equation (2) and replace in equation (1)

`\begin{gathered} 30=x+y \\ \text{subtract y in both sides} \\ 30-y=x+y-y \\ 30-y=x \end{gathered}`

replace the x value in equation(1)

`\begin{gathered} 8=(x)/(y)\rightarrow equation(1) \\ 8=(30-y)/(y) \\ \text{cross multiply} \\ 8y=30-y \\ 8y+y=30 \\ \text{9y}=30 \\ y=(30)/(9) \\ y=(10)/(3) \\ \\ \end{gathered}`

replace the y value in equation (2)

`\begin{gathered} 30=x+y\rightarrow equation(2) \\ 30=x+(10)/(3) \\ \text{subtract 10/3in both sides} \\ 30-(10)/(3)=x+(10)/(3)-(10)/(3) \\ (80)/(3)=x \end{gathered}`

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