Atraveler buys $1600 in traveler's checks, in $10, $20, and $50 denominations. the number of $10 checks is 5 less than twice the number of $20 checks, and the number of $50 checks is 3 less than the number of $20 checks. how many checks of each type are there?

1) Let's say that the number of $10 denominations is x, $20 is y, and $50 is z.
2) "The number of $10 checks is 5 less than twice the number of $20 checks" This means x = 2y-5.
3) "...the number of $50 checks is 3 less than the number of $20 checks." This means z = y-3.
4) "A traveler buys $1600 in traveler's checks" which means that ($10)x+($20)y+($50)z = $1600.
5) Use the first and second equations to plug into the third because they are both in terms of y: (10)(2y-5)+(20)y+(50)(y-3) = 1600
6) Distribute: (20y-50)+(20y)+(50y-150) = 1600.
7) Combine like terms: 20y+20y+50y-50-150=1600 => 90y-200 = 1600
8) Add 200 to both sides: 90y = 1800
9) Divide both sides by 90 to find y.
10) y = 20