Although it is impossible to make a pile of money worth exactly $3, it is still possible to buy something that costs $3. You can give two $7 bills to the cashier and receive one $11 bill as change. (2x7-11=3) *Find all amounts that cannot be used as prices because they are impossible to make out of $7 and$11 bills if you can get change when making a purchase. * is there a greatest impossible price beyond which all prices are possible? if not, why not? if so, can you explain why all prices beyond that price are possible? This is in a land with only $7 and $11 bills.

Question

Although it is impossible to make a pile of money worth exactly $3, it is still possible to buy something that costs $3. You can give two $7 bills to the cashier and receive one $11 bill as change. (2x7-11=3)   *Find all amounts that cannot be used as prices because they are impossible to make out of $7 and$11 bills if you can get change when making a purchase. * is there a greatest impossible price beyond which all prices are possible? if not, why not? if so, can you explain why all prices beyond that price are possible?  This is in a land with only $7 and $11 bills.

anonymous · Answer

Are you sure? I tried to work it out and i can get any price. 1- infinety

hero · Answer

Okay, I found the answer you are looking for: 

If the greatest common divisor of 2 two numbers, a and b is 1, then linear combinations of a and b will produce ANY integer.