A fitness center surveyed its members regarding their primary exercise routine. Of the mem… — ACT

A fitness center surveyed its members regarding their primary exercise routine. Of the members surveyed, $\frac{1}{4}$ chose strength training, $0.35$ chose cardio workouts, and $15\%$ chose group fitness classes. The remaining $75$ members chose swimming. What is the total number of members surveyed by the fitness center?

A
100
B
200
C
250
300Answer
E
500

Answer

300

Converting

\frac{1}{4}

25\%

and

0.35

35\%

, the three specified groups represent

25\% + 35\% + 15\% = 75\%

of the total members. Consequently, the remaining

25\%

of members choose swimming. Since

25\%

(or

\frac{1}{4}

) of the total surveyed group equals 75 members, multiplying 75 by 4 gives a total of 300 members.

Step-by-Step Solution

Convert all given proportions to a common format (percentages or decimals)

Strength training =

\frac{1}{4} = 25\%

; Cardio workouts =

0.35 = 35\%

; Group fitness =

15\%

Converting all amounts to percentages allows for direct addition.

Calculate the total percentage accounted for by the first three categories

25\% + 35\% + 15\% = 75\%

Combining these parts determines what fraction of the total surveyed group is already accounted for.

Determine the percentage corresponding to the remaining members who chose swimming

100\% - 75\% = 25\%

The remaining members represent the remaining portion of the whole.

Set up an equation to find the total number of members (

T

)

0.25 T = 75 \implies T = \frac{75}{0.25} = 300

Dividing the part by its corresponding decimal percentage yields the total population.

Key Concept

Converting between fractions, decimals, and percentages to calculate an unknown total quantity

Estimated Time:1m 15s

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