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Tickets to the zoo cost $4 for children, $5 for teenagers, and $6 for adults. In the high season, 1200 people come to the zoo every day. On a certain day, the total revenue at the zoo was $5300. For every three teenagers, eight children went to the zoo. How many teenagers, children, and adults went to the zoo?

Correct answer:

a =  100
c =  800
t =  300

Step-by-step explanation:


6a + 5t + 4c = 5300
a + t + c = 1200
(8/3)t = c

6·a + 5·t + 4·c = 5300
a + t + c = 1200
(8/3)·t = c

6a+4c+5t = 5300
a+c+t = 1200
3c-8t = 0

Row 2 - 1/6 · Row 1 → Row 2
6a+4c+5t = 5300
0.333c+0.167t = 316.667
3c-8t = 0

Pivot: Row 2 ↔ Row 3
6a+4c+5t = 5300
3c-8t = 0
0.333c+0.167t = 316.667

Row 3 - 0.33333333/3 · Row 2 → Row 3
6a+4c+5t = 5300
3c-8t = 0
1.056t = 316.667


t = 316.66666667/1.05555556 = 300
c = 0+8t/3 = 0+8 · 300/3 = 800
a = 5300-4c-5t/6 = 5300-4 · 800-5 · 300/6 = 100

a = 100
c = 800
t = 300

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