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# Now a long one

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On planet Enigma, the residents use a currency called the confusion. There are only 2 confusion bills on Enigma, one worth 8 confusions and the other worth 11 confusions. There are also some coins of smaller value, but each weighs over 10 kilograms, so they are difficult to carry around.
Vendors do not give change.

a. In how many ways can a resident of Enigma use only bills to purchase a toaster that costs 96 confusions?

b. In how many ways can a resident of Enigma use only bills to purchase a gyroscope that costs 97 confusions?

c. In how many ways can a resident of Enigma use only bills to purchase a single math book page that costs 69 confusions? (A page is so expensive because the residents of Enigma clearly don't understand much math.)

Apr 6, 2019

#1
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I will take a crack at this one!

I think what they want you to do is to solve the following equations:

11n  +  8m = 96...............(1)

11n  +  8m = 97...............(2)

11n  +  8m = 69...............(3)

Each of the above equations has an infinite number of solutions. Example: The first equation can be solved using n = 8 and m = 1 and thereafter, any multiple of n such as n = 16 and m = -10 (in the sense that you will pay: 16 x 11 confusions=176 - 96 = 80 / 8 confusions =10 that you will get back, and so on....).

The above method applies to all 3 equations above.

Apr 6, 2019
#2
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Could you explain more? Thank you