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A recreation center surveyed 420 members about two activities: swimming and cardio-machine workouts. Of the members surveyed, 160 met a 2-hour-per-week mark for both activities, 80 met the mark for cardio-machine workouts but not for swimming, and for every member who met the mark for neither activity, 5 met the mark for swimming but not for cardio-machine workouts. How many of the 420 members met the 2-hour-per-week mark for neither activity?
A. 30
B. 80
C. 150
D. 180
E. 260
A. 30
B. 80
C. 150
D. 180
E. 260
07 Aug 2026, 04:56
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Official Solution:
A recreation center surveyed 420 members about two activities: swimming and cardio-machine workouts. Of the members surveyed, 160 met a 2-hour-per-week mark for both activities, 80 met the mark for cardio-machine workouts but not for swimming, and for every member who met the mark for neither activity, 5 met the mark for swimming but not for cardio-machine workouts. How many of the 420 members met the 2-hour-per-week mark for neither activity?
A. 30
B. 80
C. 150
D. 180
E. 260
Let \(x\) be the number of members who met the 2-hour-per-week mark for neither activity.
Then the number of members who met the mark for swimming but not for cardio-machine workouts, that is, swimming only, is \(5x\).
The 420 members are split into four groups:
• Both activities: 160
• Cardio-machine workouts only: 80
• Swimming only: \(5x\)
• Neither activity: \(x\)
So:
\(160 + 80 + 5x + x = 420\)
\(6x = 180\)
\(x = 30\)
Therefore, 30 members met the 2-hour-per-week mark for neither activity.
Answer: A
A recreation center surveyed 420 members about two activities: swimming and cardio-machine workouts. Of the members surveyed, 160 met a 2-hour-per-week mark for both activities, 80 met the mark for cardio-machine workouts but not for swimming, and for every member who met the mark for neither activity, 5 met the mark for swimming but not for cardio-machine workouts. How many of the 420 members met the 2-hour-per-week mark for neither activity?
A. 30
B. 80
C. 150
D. 180
E. 260
Let \(x\) be the number of members who met the 2-hour-per-week mark for neither activity.
Then the number of members who met the mark for swimming but not for cardio-machine workouts, that is, swimming only, is \(5x\).
The 420 members are split into four groups:
• Both activities: 160
• Cardio-machine workouts only: 80
• Swimming only: \(5x\)
• Neither activity: \(x\)
So:
\(160 + 80 + 5x + x = 420\)
\(6x = 180\)
\(x = 30\)
Therefore, 30 members met the 2-hour-per-week mark for neither activity.
Answer: A
