A bank teller has a total of 74 bills in five-, ten-, and twenty-dollar denominations. The total value of the money is $920. (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. x+y+z = 74 5x + 10y + 20z = 920 (Do not factor. Use integers or decimals for any numbers in the expressions.) There are a total of solutions.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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(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 bank teller has a total of 74 bills in five-, ten-, and twenty-dollar denominations. The total value of the money is $920.
(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.
x+y+z = 74
5x + 10y + 20z = 920
(Do not factor. Use integers or decimals for any numbers in the expressions.)
There are a total of solutions.
Transcribed Image Text:A bank teller has a total of 74 bills in five-, ten-, and twenty-dollar denominations. The total value of the money is $920. (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. x+y+z = 74 5x + 10y + 20z = 920 (Do not factor. Use integers or decimals for any numbers in the expressions.) There are a total of solutions.
Expert Solution
Step 1

a)

Given that,

x+y+z=74                        15x+10y+20z=920                      2

Multiply the equation (1) with 5 and subtract it from (2) as follow,

5x+10y+20z-5x+5y+5z=920-3705x+10y+20z-5x-5y-5z=5505y+15z=550y+3z=110y=110-3z

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