Question

a baseball team has home games Thursdays and Sunday the two games together earn 3917.50 Thursday game generates 509.50 less than Sundays game how much money was taken in at each game

Answer 1

Set x = thursday
Set y = Sunday

x+y = 3917.50
You know that Thursday earns 509.50 less, so it means that if earning 509.5 more on Thurs would equate to the amount earned on Sunday.
x+ 509.50 = y
Substitute to the first equation for y:
x + (x+ 509.50) = 3917.50
2x = 3408
x = 1704 dollars.
Remember that x is thursday. So the amount earned on Sunday would be:
x + 509.5
= 1704 + 509.5
= 2213.5

Let's check
2213.5 - 1704 = 509.5 checked right difference
2213.5 + 1704 = 3917.5 checked