Percent of desired things times total number of things is number of desired things. Percent is number divided by 100.
For the playground: 5/100 * 80 = 4 teachers. The ratio of teachers to people is 4/80 = 1/20.
For the gym: 15/100 * 60 = 9 teachers. The ratio of teachers to people is 9/60 = 3/20.
The gym has the higher ratio.
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