Question

Percentages

a. The labels on U-Turn protein energy bars include the statement that these bars contain “125% less fat than the leading chocolate candy brands” (based on data from Consumer Reports magazine). What is wrong with that claim?

b. In a Pew Research Center poll on driving, 58% of the 1182 respondents said that they like to drive. What is the actual number of respondents who said that they like to drive?

c. In a Pew Research Center poll on driving, 331 of the 1182 respondents said that driving is a chore. What percentage of respondents said that driving is a chore?

Short answer

a. 100% implies no fat content. Thus, 125% is not meaningful.

b. 686

c. 28%

Step-by-step solution

Step 1:Interpret the percentage clearly

a.

Given: U-Turn bars claim to contain “125% less fat than the leading chocolate candy brands.”

The statement is wrong.

100% less fat than leading chocolate candy brands implies no fat content in U-Turn protein bars.

125%, as a result, implies a situation beyond zero fat content, which is not possible.

Step 2:Find the actual count from percentages

b.

Given: The total number of respondents is1182. Of these, 58% mentioned that they like to drive.

The multiplication by 100 for a fraction of counts and total results in percentages.

Let x be the actual count of respondents who said that they like to drive.

Thus, the following holds true.

\(\begin{array}{c}\frac{x}{{1182}} \times 100 = 58\\x = \frac{{58 \times 1182}}{{100}}\\x = 685.56\\x \approx 686\end{array}\)

Note: 685.56 respondents are not possible.

Thus, 686 respondents form the actual count for those who said they liked driving.

Find the percentage equivalent of the count

c.

Given: The total number of respondents is 1182. Of these, 331 said that driving is a chore.

The fraction of respondents who said driving is a chore is\(\frac{{331}}{{1182}}\).

The percentage equivalent of the fraction is computed by multiplying the fraction by 100as shown below:

\(\frac{{331}}{{1182}} \times 100 = 28.0034\% \)

Thus, the percentage of respondents who said driving is a chore is approximately 28%.