Final answer:
To solve for the number of $1 bills and other denomination bills Harvey has, we set up a system of linear equations representing the number of bills and their total value. By solving the system, we determine that Harvey has 2 $1 bills and 4 $5 bills.
Step-by-step explanation:
The student's question involves solving a system of linear equations to determine the number of $1 bills and other denomination bills that Harvey has. Since Harvey has 6 bills that total $22, we can use variables to represent the quantities of each denomination, then create and solve a system of equations. Let's define x as the number of $1 bills and y as the number of the other denomination bills.
- Express the total number of bills: x + y = 6 (since Harvey has 6 bills in total).
- Express the total value of the bills: x + 5y = 22 (assuming the other denomination is $5, as Harvey could not have higher denominations for the sum to be 22).
- Subtract the first equation from the second to find y: (x + 5y) - (x + y) = 22 - 6, simplifying to 4y = 16, therefore, y = 4.
- Substitute y = 4 into the first equation to find x: x + 4 = 6, so x = 2.
- Therefore, Harvey has 2 $1 bills and 4 $5 bills.