A carnival charges two different prices for admissions. Adults cost $4 while children cost $1.50. If a total of $5050 was collected for 2200 tickets, how many of each ticket was sold?

Answer:Step-by-step explanation:We have to have 2 different equations to solve this.  One equation will represent the number of tickets sold while the other represents the money collected when the tickets were sold.We know that adult tickets + children tickets = 2200 tickets.That's the "number of tickets" equation.  Let's call adult tickets "a" and children's tickets "c".  So a + c = 2200Now if each adult costs $4, then the expression that represents that as a cost is 4a.  If there is 1 adult, the cost is $4(1) = $4; if there are 2 adults, the cost is $4(2) = $8; if there are 3 adults, the cost is $4(3) = $12, etc.The same goes for the children's tickets.  If each child's ticket is $1.50, then the expression that represents the cost of a child's ticket is 1.5c (we don't need the 0 at the end; it doesn't change anything to drop it off).  The total money brought in from the cost of these tickets was $5050, so4a + 1.5c = 5050Let's solve the first equation for a.  If a + c = 2200, then a = 2200 - c.  Sub that into the second equation and solve it for c:4(2200 - c) + 1.5c = 5050 and8800 - 4c + 1.5c = 5050 and-2.5c = -3750 soc = 1500That means that there were 1500 children's tickets sold.  If a + c = 2200, then a + 1500 = 2200 soa = 2200 - 1500 soa = 700There were 1500 children's tickets sold and 700 adult tickets sold.