A bank teller has a total of 63 bills in​ five-, ten-, and​ twenty-dollar denominations. The total value of the money is $730. (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.   ​(a) Let x be the number of​ five-dollar bills, y be the number of​ ten-dollar bills, and z be the number of twenty dollar bills. Translate the given information into two​ equations, using​ x, y, and z as the variables.   ______=63 ______=730   Thus, the solution with the largest number of​ five-dollar bills is when the bank teller has_____fives,______​tens, and_______twenties.   (Do not factor. Use integers or decimals for any numbers in the​ expressions.)

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