Question

The number of people estimated to vote in an election was 7,000. The actual number of people who voted was 5,600.Part A By what percent did the estimate vary from actual turnout? Part B In the previous election 6,400 people voted. What is the percent decrease in actual voters?

Answer 1

Step 1

Part A

Write an expression in ratio form that can be used to determine the percent with which the estimate varied from the actual turnout

Estimate to vote = 7,000 people

Actual turnout = 5,600 people

The ratio is given as

`\frac{estimated\text{ number of people to vote}-\text{actual number of peple that voted}}{\text{actual number of people that voted}}*100`

Step 2

Substitute and get the answer to step 1

`\begin{gathered} =(7000-5600)/(5600)*100 \\ =(1400)/(5600)*100 \\ x=\text{ 25\%} \end{gathered}`

Hence the percent with which the estimate varied with the actual turnout =25%

Step 3

Calculate the percentage decrease

State an expression for percentage decrease

`Percentage\text{ decrease =100}*\frac{\text{final}-\text{initial}}{\text{initial}}`

Step 4

Substitute and get the answer to part

`\text{Percentage decrease = 100}*(5600-6400)/(6400)`
`\text{percentage decrease =12.5\%}`

The percentage decrease in the actual voters = 12.5%