When a family with 2 adults and 3 children bought tickets for an amusement park, they paid a total of $56.50. The next family, with 4 children and one adult, paid$49.50. What was the price of an adult ticket and a child ticket using system of equations.

c=child
Equation 1 (the first family)
2a+3c=56.5
Equation 2 (the second family)
a+4c=49.5 multiply by 2
2a+8c=99  multiply by -1
-2a-8c=-99
Systems of Equations
(2a+3c=56.5)
+  (-2a-8c=-99)
-
-5c=-42.5
c=$8.5 Substitute 2a+3*8.5=56.5 2a+25.5=56.5 2a=31 a=$15.5
Conclusion
Adult Ticket: $15.5 Child Ticket:$8.5

The cost of an adult ticket is $15.50 and the cost of a child ticket is$8.50
Proof:
Set up a system of equations calling Adults a and Children c
2a+3c= $56.50 (equation 1) 4c+a=$49.50 (equation 2)
a= -4c+49.50 (i subtracted 4c to both sides) (label equation 3)
sub equation 3 into equation 1
2(-4c+49.50)+3c= 56.50
-8c+99+3c=56.50
-5c+99=56.50
-99    -99
-5c = -42.50
c= -42.50/ -5
c= 8.50
sub c=8.50 into equation 3 to find adult price
a= -4(8.5)+49.50
a= 15.50

Therefore Child Cost = $8.50 and Adult Cost=$15.50

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