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September 17th, 2014, 03:12 AM   #1
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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 twenty-dollar 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 five-dollar bills
(c) Find the solution with the largest number of five-dollar bills

Thanks
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September 17th, 2014, 03:37 AM   #2
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Let $x$, $y$ and $z$ be the number of five-, ten- and twenty-dollar 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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