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Money bag

Money bag


We have 26 bills in a bag. If we randomly take 20 bills from the bag, we will have at least one 1 dollar bill, two 2 dollar bills and 5 5 dollar bills.

How much money is in the bag?

Solution

We will represent the 1 dollar bills with the letter "A", the two dollar bills with the letter "B" and the 5 dollar bills with the letter "C".

We know that the bag contains 26 bills, so if we take 20, 6 will remain and the following conditions will be met:

A ≥ 6 + 1 = 7
B ≥ 6 + 2 = 8
C ≥ 6 + 5 = 11

From here we deduce that A + B + C ≥ 26. Since we know that there are 26 bills in the bag, it must be fulfilled that A + B + C = 26 and therefore A = 7, B = 8 and C = 11. The total amount will be (7 x 1) + (8 x 2) + (11 x 5) = 78 dollars.