Whenever Deven and Laura owe each other money, they "pay" each other using stickers. They've agreed that a Harry Potter sticker is worth 49 dollars and a Twilight sticker is worth 35 dollars. They can even use stickers as "change" if one person overpays the other. For example, if Deven owes Laura 189 dollars, he can give her 6 Harry Potter stickers ( dollars), and she can return 3 Twilight stickers ( dollars). This trade is like a transfer of dollars. What is the smallest positive debt, in dollars, that can be paid off using sticker trading?
+33616 Positive difference = 49m - 35n. where m and n are integers.
The greatest common factor of 49 and 35 is 7, so this is the smallest positive debt possible.
For example, if Devon owed Laura 7 dollars, he could give her 3 Harry Potters = 147 dollars, and she could give him 4 Twilights = 140 dollars in return.
35 = 5 * 7, and
49 = 7^2, Therefore the LCM of {35, 49} =
7^2 *5 = 245 - This is smallest positive debt in this scheme.
+33616 Positive difference = 49m - 35n. where m and n are integers.
The greatest common factor of 49 and 35 is 7, so this is the smallest positive debt possible.
For example, if Devon owed Laura 7 dollars, he could give her 3 Harry Potters = 147 dollars, and she could give him 4 Twilights = 140 dollars in return.
