Two groups of people visited an amusement park. A group of8 children and 4 adults paid $856 for their tickets. A different grouof 2 children and 4 adults paid $508. What was the cost of a ticketfor an adult?

Accepted Solution

Answer:8.5 or 8.50Step-by-step explanation:The cost of an adult ticket is $15.50 and the cost of a child ticket is $8.50Proof:Set up a system of equations calling Adults a and Children c2a+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 12(-4c+49.50)+3c= 56.50-8c+99+3c=56.50-5c+99=56.50     -99    -99-5c = -42.50c= -42.50/ -5c= 8.50sub c=8.50 into equation 3 to find adult pricea= -4(8.5)+49.50a= 15.50Therefore Child Cost = $8.50 and Adult Cost= $15.50 ora=adultc=childEquation 1 (the first family)2a+3c=56.5Equation 2 (the second family)a+4c=49.5 multiply by 22a+8c=99  multiply by -1-2a-8c=-99Systems of Equations    (2a+3c=56.5)+  (-2a-8c=-99)-------------         -5c=-42.5             c=$8.5Substitute2a+3*8.5=56.52a+25.5=56.52a=31a=$15.5ConclusionAdult Ticket: $15.5Child Ticket: $8.5