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September 17th, 2014, 03:12 AM  #1 
Newbie Joined: Sep 2014 From: New York Posts: 1 Thanks: 0  Systems of Linear Equations  Word Problem involving
Hi Everyone Can someone please help me out on the following word problem  been trying to solve this for hours and I can't find answer(s) that make sense A bank teller has a total of 70 bills in five, ten and twentydollar denominations. The total value of the money is $960. (a) Find the total number of solutions (b) Find the solution with the smallest number of fivedollar bills (c) Find the solution with the largest number of fivedollar bills Thanks 
September 17th, 2014, 03:37 AM  #2 
Senior Member Joined: Dec 2013 From: Russia Posts: 327 Thanks: 108 
Let $x$, $y$ and $z$ be the number of five, ten and twentydollar bills, respectively. Form two equations saying that the total sum is \$960 and the number of bills is 70. Use them to express $x$ and $y$ through $z$. For each $z$, the corresponding values of $x$ and $y$ form a solution of the two equations. You need to observe two restrictions: each of $x$, $y$ and $z$ is an integer and is between 0 and 70. So draw the graphs of $x(z)$ and $y(z)$ and for $0\le z\le 70$ find the interval of $z$ where $0\le x,y\le 70$. The number of integer $z$ in that interval equals the number of solutions.


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