Question

Francisco is working two summer jobs, making $15 per hour life guarding and making $8 per hour clearing tables. In a given week, he can work at most 8 total hours and must earn no less than $80. If x represents the number of hours lifeguarding and y represents the number of hours clearing tables, write and solve a system of inequalities graphically and determine one possible solution.

Answer 1

The system of inequalities is:

x + y ≤ 8 (1)

5x +8y ≥ 80 (2)

The graphical solution is attached and one possible solution is (-30,30).

What is inequality?

The relation between two unequal expressions is defined as inequality.

Given that, the person makes $15 per hour of lifeguarding and $8 per hour clearing tables.

It is also given that x represents the number of hours of lifeguarding and y represents the number of hours of clearing tables.

The person has at most 8 hours a week, therefore, it follows:

x + y ≤ 8 (1)

The earnings of the person in a week are:

15x + 8y

Since the earnings must be no less than $80, it follows:

15x +8y ≥ 80 (2)

Hence, the system of inequalities is:

x + y ≤ 8 (1)

5x +8y ≥ 80 (2)

The graphical solution is attached and one possible solution is (-30,30).

Answer 2

Francisco works life guarding at $15 per hour and clearing tables at $8 per hour, with a maximum of 8 weekly hours and a minimum earning of $80. Graphing inequalities yields feasible solutions. The point marked on the graph by overlapping inequalities represent a possible solution.

Let x represent the number of hours Francisco spends life guarding and y represent the number of hours he spends clearing tables. The conditions can be expressed as inequalities:

1. The total hours worked must be at most 8 hours:

`\[ x + y \leq 8 \]`

2. He must earn no less than $80:

`\[ 15x + 8y \geq 80 \]`

To find one possible solution, you can graph these inequalities on a coordinate plane. The shaded region where these inequalities overlap represents the feasible solutions. A point within this region will be a valid solution. The point marked on the graph by overlapping inequalities represent a possible solution.