Question

A student earns money during the summer by charging $25 per hour tutoring neighborhood kids and $35 per hour cutting their neighbor's grass. The student cannot work more than 35 hours per week. Let x represent the number of hours tutoring kids in the neighborhood and y represent the number of hours spent cutting grass his neighbor’s grass. Write a system of inequalities that represents the given constraints. The student wants to earn at least $475 each week.

Answer 1

Step-by-step explanation:

The student's question about summer earnings can be represented with the following system of inequalities: 25x + 35y ≥ 475 to ensure at least $475 earnings per week, x + y ≤ 35 to not exceed 35 working hours per week, and x ≥ 0, y ≥ 0 to avoid negative working hours.

Answer 2

The student's question about summer earnings can be represented with the following system of inequalities: 25x + 35y ≥ 475 to ensure at least $475 earnings per week, x + y ≤ 35 to not exceed 35 working hours per week, and x ≥ 0, y ≥ 0 to avoid negative working hours.

Step-by-step explanation:

To represent the constraints for the student's summer earnings with a system of inequalities, we identify the following conditions: the rate per hour for tutoring, the rate per hour for cutting grass, the maximum number of hours the student can work per week, and the minimum earnings target per week. Let x represent the number of hours spent tutoring and y represent the number of hours spent cutting grass. The system of inequalities is as follows:

• 25x + 35y ≥ 475 (The student wants to earn at least $475 per week.)
• x + y ≤ 35 (The student cannot work more than 35 hours per week.)
• x ≥ 0 (The student cannot tutor for negative hours.)
• y ≥ 0 (The student cannot cut grass for negative hours.)

These inequalities respect the student's time and earning constraints for their summer work.