Question

A bank teller has a total of 72 bills in​ five-, ten-, and​twenty-dollar denominations. The total value of the money is ​$920. 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.

​(a) Find the total number of solutions (how manny?). ​
(b) Find the solution with the smallest number of​five-dollar bills.
(c) Find the solution with the largest number of​ five-dollar bills.

Answer 1

To translate the given information into equations, we can use the following two equations: 1. x + y + z = 72 and 2. 5x + 10y + 20z = 920. We can solve this system of equations to find the total number of solutions, the solution with the smallest number of five-dollar bills, and the solution with the largest number of five-dollar bills.

Step-by-step explanation:

To translate the given information into equations, we can use the following two equations:

1. x + y + z = 72 (equation representing the total number of bills)

2. 5x + 10y + 20z = 920 (equation representing the total value of the money)

(a) To find the total number of solutions, we need to solve the system of equations. The solution to this system will give us the values of x, y, and z. If there is a unique solution, it means there is only one set of values that satisfies both equations. If there are infinite solutions, it means there are multiple sets of values that satisfy both equations. If there is no solution, it means there are no sets of values that satisfy both equations.

(b) To find the solution with the smallest number of five-dollar bills, we can minimize the value of x, while still satisfying both equations. (c) To find the solution with the largest number of five-dollar bills, we can maximize the value of x, while still satisfying both equations.