word problem help

Question

At a zoo, the price of 4 adult tickets and 6 child tickets is $77. The price of 6 adult tickets and 4 child tickets is $83. What is the ticket price for one adult and for one child?

Answer 1

4A+6C=77, so A=(77-6C)/4

6A+4C=83, so 6((77-6C)/4)+4C=83 -> (462-36C)/4 + 4C = 83 -> 115.5-9C+4C=83 -> 32.5=5C -> 6.50=C

4A+(6.50*6)=77 -> 4A+39=77 -> 4A=38 -> A=9.50

So the price for 1 adult and 1 child is 9.50+6.50 or $16