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To enter a zoo, adult visitors must pay $5, whereas children and seniors pay only half price. On one day, the zoo collected a total of $765. If the zoo had 223 visitors that day, how many half-price admissions and how many full-price admissions did the zoo collect?

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There are 83 full price and 140 half-price admissions.

There are 83 full price and 140 half-price admissions.

Two equations needed : x + y = 223 and 5x + 2.5y = 765

Use the first equation, x + y = 223 and rearrange it to fit the problem and substitute : y = 223 - x

5x + 2.5(223 - x) = 765

5x + 557.5 - 2.5x = 765

2.5x + 557.5 = 765

2.5x = 765 - 557.5

2.5x = 207.5

2.5x ÷ 2.4 = 207.5 ÷ 2.5

x = 83

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Now just subtract 223 and 83 to get the others:

223 - 83 = 140


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