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Logan is working two summer jobs, making $18 per hour tutoring and making $10 per hour clearing tables. In a given week, he can work a maximum of 13 total hours and must earn at least $170. If xx represents the number of hours tutoring and yy represents the number of hours clearing tables, write and solve a system of inequalities graphically and determine one possible solution.

Respuesta :

RoseVb30

Answer: he could work 7 hours tutoring and 6 hours clearing tables

Step-by-step explanation:

The system of inequalities can be used to find the number of hours Logan

can spend on each job in a week.

Response:

The system of inequalities are;

  • x + y ≤ 13
  • 18·x + 10·y ≥ 170

A possible solution of the system of inequality obtained from the graph is the point (5, 8)

  • x = 5, and y = 8

Methods used to solve the inequality graphically

The amount Logan makes per hour tutoring = $18 per hour

The amount he makes clearing tables = $10 per hour

Number of hours Logan can work in a week = 13

Amount he must earn in a week = At least $170

Number of hours he spends tutoring = x

Number of hours he spends clearing tables = y

Based on the given information, we have;

  • x + y ≤ 13
  • 18·x + 10·y ≥ 170

Please find attached the graph of the above inequality showing the feasible region.

A possible solution obtained from the feasible region is the point of intersection of the two inequalities which is the point (5, 8), which gives;

  • A possible solution is x = 5, y = 8

Therefore, Logan can spend 5 hours tutoring and 8 hours clearing tables in a week to work for 13 hours and make $170.

Learn more about inequalities here:

https://brainly.com/question/8284035

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