Explanation:
a = price for 1 adult ticket
c = price for 1 child ticket
4a + 6c = 77
6a + 4c = 83
let's multiply the first equation by -3/2 and then add both equations :
-6a - 9c = -231/2 = -115.5
6a + 4c = 83
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0 -5c = -32.5
5c = 32.5
c = $6.50
6a + 4×6.5 = 83
6a + 26 = 83
6a = 57
a = 57/6 = $9.50
one adult ticket = $9.50
one child ticket = $6.50