Thread: Traveler's Checks

A tourist purchased a total of 1500 dollars worth of traveler's checks in 10 dollars and 50 dollars denominations. During the trip the tourist cashed 7 checks and then lost all of the rest. If the number of 10 dollar checks cashed was one more or one less than the number of 50 dollar checks, what is the minimum possible value of the checks that were lost?

1500 - 70 = 1430
1430 - 50 = 1380
1380 - 70 = 1310

My answer is 1310 dollars.

The book's answer is 1270 dollars.

I got lost in the application in terms of the word OR in the following statement:

If the number of 10 dollar checks cashed was one more or one less than the number of 50 dollar checks, what is the minimum possible value of the checks that were lost?

Why is my answer wrong? Can someone set up an equation for me to solve?

let $n$ be the number of \$10 checks cashed

Either

$n+(n+1) = 7 \Rightarrow n = 3$

or

$n + (n-1) = 7 \Rightarrow n = 4$

The amount lost will be

$1500 - 3(10) - 4(50) = 1500 - 230 = 1270$

or

$1500 - 4(10) - 3(50) = 1500 - 190 = 1310$

$1270 < 1310$ and is thus the minimum possible value of the amount lost.

Originally Posted by romsek

let $n$ be the number of \$10 checks cashed

Either

$n+(n+1) = 7 \Rightarrow n = 3$

or

$n + (n-1) = 7 \Rightarrow n = 4$

The amount lost will be

$1500 - 3(10) - 4(50) = 1500 - 230 = 1270$

or

$1500 - 4(10) - 3(50) = 1500 - 190 = 1310$

$1270 < 1310$ and is thus the minimum possible value of the amount lost.

You lost me in terms of the two equations you posted after the word EITHER with respect to n.

Originally Posted by harpazo

You lost me in terms of the two equations you posted after the word EITHER with respect to n.

you are told that the number of \$10 checks cashed was either one more or one less than the number of \$50 checks cashed.

you don't know which so you have to investigate both possibilities.

Originally Posted by romsek

you are told that the number of \$10 checks cashed was either one more or one less than the number of \$50 checks cashed.

you don't know which so you have to investigate both possibilities.

Why did you equate both equations to 7?

Originally Posted by harpazo

Why did you equate both equations to 7?

Do you even read the problems you post before posting them?

The problem very clearly states that the tourist cashed 7 of the checks and lost the rest.

Now, now, Romsek, do you not know that Harpazoo works long shifts, and is tired...

Originally Posted by romsek

Do you even read the problems you post before posting them?

The problem very clearly states that the tourist cashed 7 of the checks and lost the rest.

Yes, I read every question several times before posting. In fact, I only post questions AFTER trying to solve on my own.