Question

A staffing agency for in-home nurses and support staff places necessary personnel at locations on a daily basis. Each placed nurse works 240 minutes per day at a daily rate of $90. Each support staff employee works 360 minutes per day at a daily rate of $120.

A. On a given day, 3000 total minutes are worked by then nurses and support staff that were placed. Write an equation that represents this relationship
B. On the same day, earnings for placed nurses and support staff totaled $1050. Write an equation that represents this relationship.
C. Solve the system of equations, and interpret the solution in the context of the situation.

Answer 1

The equation representing the total minutes worked by nurses and support staff is 240x + 360y = 3000, while the equation representing the earnings for placed nurses and support staff is 90x + 120y = 1050. The system of equations can be solved to determine the number of nurses and support staff placed on that day.

Step-by-step explanation:

A. Let x represent the number of nurses and y represent the number of support staff. Since each nurse works 240 minutes and each support staff works 360 minutes, the total minutes worked by nurses and support staff on a given day can be expressed as the equation 240x + 360y = 3000.

B. The earnings for placed nurses and support staff on that day can be represented by the equation 90x + 120y = 1050.

C. To solve the system of equations, we can use the method of substitution or elimination. Solving these equations will give us the values of x and y, which represent the number of nurses and support staff. The solution will provide insights into the number of each personnel that were placed on that day.