(a word problem)
If marissa has exactly $61 dollars, and one dollar, five dollar and ten dollar bills. She has 14 bills. How many of each bill does she have?
I'd start with 11 ones, leaving $50 for remaining 3 bills.
Looks like two $20's and a $10 will do it -- whoops! NO $20's allowed.
Try 6 ones, leaving $55 for remaining 8 bills.
Looks like five $5's and three $10's will do it. Best wishes
First you should use the smallest bill to until you get to a difference that is divisible by both of the larger denominations. Set this amount aside because you know these bills will definitely be in the final count. Then use the largest denomination to get the difference in the $61 and the amount of money you have in the pile of money you set aside. Count the number of bills you have total (using the largest bills and the smallest bills that you set aside). For every $10 bill that is turned into 2 $5 bills, the total number of bills goes up by 1 because you have 2 bills now, but you gave away 1 bill to get those 2 so you gained 1 less than the total you traded for. So for every $5 bill turned into $1 bills, the total number of bills used goes up by 4 - you got 5 bills, but you had 1 to start with, so you only gained 4 bills to have the same amount of money. Continue turning larger bills into smaller bills until you have the total number of bills necessary.