Question

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.

Answer 1

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=370→x+y-x=370-x→y=370-x

b) Replacing y=370-x in the second equation:
2) 3x+7y=1750→3x+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-x→y=370-210→y=160

Answer:
The number of child tickets was 210 and
the number of adult tickets was 160