Please your problem can be modeled with the subsequent system:

3 a + 4 c = 121

2a + 3 c = 86

where a is the price of adult's ticket and c is the price of children's ticket

from first equation I get:

c = 121/4 - 3a/4

then substituting itnot the second equation I can write:

8a +363 - 9a =344

and

a = 19

so

c = 121/4 - 57/4 = 16

then price of adult's ticket = $19

price of children's ticket = $16

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