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?

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Step-by-step explanation:

Let t represent the third-place prize value. Then the first place prize has a value of 2t+500, and the second-place prize is 2t+100. The total value of the three prizes is ...

  t +(2t+500) +(2t+100) = 1850

  5t +600 = 1850

  5t = 1250

  t = 250 . . . . . . . . . . . third place prize

  2t +500 = 1000 . . . . first place prize

  1000 -400 = 600 . . .second place prize

The prizes for 1st, 2nd, and 3rd places are $1000, $600, and $250, respectively.

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