A contest gives out prizes for first, second, and third place. First place is $\$500$ more than double third place. Second place is $\$400$ less than first place. All together, $\$1850$ is given out in prizes. How much is each prize worth?
3rd place = x
1st place = 2x + 500
2nd place = (2x + 500) - 400 = 2x + 100
So
x + ( 2x + 500) + (2x + 100) = 1850
5x + 600 = 1850
5x = 1850 - 600
5x = 1250
x = 1250 / 5 = $ 250 = 3rd place
2(250) + 100 = $ 600 = 2nd place
2(250) + 500 = $1000 = 1st place