Question

Tom purchased a total of $5000 worth of traveler's checks in $50 and $100 denominations for his vacation. During his vacation Tom cashed 14 checks and then lost all the rest. If the number of $50 checks cashed was two more or two less than the number of $100 checks cashed, what is the maximum possible value of checks that were lost? $3800 $3900 $4000 $4100​

Answer 1

$4000

Step-by-step explanation:

Let the number of $50 checks purchased be F and number of $100 checks purchased by H

Value of checks purchased = $5000

Let number of $50 checks cashed be F and number of $100 checks cashed be H In order to find maximum possible value of checks lost, we have to find the minimum value of checks cashed since

Value of checks lost = Value of checks purchased - Value of checks cashed

Value of checks cashed = 50F + 100H and we must minimize this value

We know F + H = 14 (1)

and either F-H = 2 or H-F = 2 or F = H-2

Case A: $50 checks cashed 2 more than $100 checks cashed

F = H + 2

Substituting for F in (1) we get (H + 2) + H = 14 => H = 6 and F = 8

Value of cashed checks = 50 * 8 + 6 * 100 = $1000

Case B: $50 checks cashed 2 less than $100 checks cashed

F = H - 2,

Substituting for F in (1) we get

(H - 2) + H = 14 => H = 8, F = 6

Value = 800 + 300= $1100

1000 < 1100 so the relationship between H and F is

F = H-2 with H = 8 and F = 6

Max. value of checks lost = 5000 - 1000 = $4000