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.

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