A traveler 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?

Question

Ladybug

Mathematics

30 September, 22:35

A traveler 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?

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Demarcus Gilbert · Answer 1

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