SOLUTION: A bank teller needs to pay out $75 using $5 bills and $20 bills. Find all possibilities for the number of each type of bill the teller could use.

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Question 774165: A bank teller needs to pay out $75 using $5 bills and $20 bills. Find all possibilities for the number of each type of bill the teller could use.
Answer by josgarithmetic(39628) About Me  (Show Source):
You can put this solution on YOUR website!
Use x for the $5 size and y for the $20 size count of each bill type.
5x%2B20y=75 and you want only whole number possibilities.
Simplify...x%2B4y=15
The count of x should be more than the count of y, so you could just solve the equation for y, and check the whole number results for x values starting at 1. Some will work and some will fail.

The easier way to do this is start with 75%2F5=15 of the $5 bills, and successively step-wise subtract $20 value as 4 of the $5 bills until no more can be substituted.

Each
Bill
Count____$5______$20
------------------------------
_________15______0
_________11______1
_________7_______2
_________3_______3