Question

A child care company charges $275 per month for children who attend part-time and $435 per month for children who attend full time. This month, they have 35 children registered for a total fee of $12,985.

Let x represent the number of children who attend full time and y represent the number of children who attend part-time. Which system of equations could be used to model this situation?

Answer 1

The system of equations to model the number of children attending full-time and part-time at a child care company, and the total fees collected is x + y = 35 and 435x + 275y = 12,985.

Step-by-step explanation:

The situation presented can be modeled by a system of linear equations based on the number of children attending the child care company part-time and full-time. We have two variables, x representing the number of full-time children and y representing the number of part-time children. The total number of children is 35, and the total amount collected in fees is $12,985.

The first equation comes from the total number of children, which is 35. So we have x + y = 35. The second equation comes from the total amount of fees collected. The fee for full-time attendance is $435, and for part-time, it's $275. Therefore, the equation is 435x + 275y = 12,985.

The system of equations to model this situation is:

1. x + y = 35
2. 435x + 275y = 12,985