On Sunday, 370 people bought tickets to the county fair. Tickets cost $7 for adults and $3 for children. The total revenue from ticket sales on Sunday was $1750. The system of equations below represents the number of people and total sales for the county fair on Sunday, where x represents the number of child tickets and y represents the number of adult tickets.
Accepted Solution
A:
Number of child tickets: x Number of adult tickets: y
1) x+y=370 2) 3x+7y=1750
Using the method of substitution a) Isolating y in the first equation: 1) x+y=370βx+y-x=370-xβy=370-x
b) Replacing y=370-x in the second equation: 2) 3x+7y=1750β3x+7(370-x)=1750
c) Solving for x: Distributive property: 3x+7(370)-7x=1750 3x+2590-7x=1750
Adding similar terms: -4x+2590=1750
-4x+2590-2590=1750-2590 -4x=-840
Dividing both sides of the equation by -4: -4x/(-4)=-840/(-4) x=210
Replacing x=210 in the first equation: 1) y=370-xβy=370-210βy=160
Answer: The number of child tickets was 210 and the number of adult tickets was 160