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Let k represent the cost of supplies, b the number of bottles, and c the number of cans. You know that the total cost is found by adding the number of bottles multiplied by the price of each to the number of cans multiplied by their unit price. (This is the computation performed anytime you purchase something.)
There are no constants in this equation.
and
. So we have a remainder of
and
. Subtracting this from the previous remainder gives a new remainder
and
. Subtracting this from the previous remainder gives a new one of
and we're done since 2 does not divide . So we have