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Ian is working two summer jobs, making $19 per hour lifeguarding and making $9 per hour clearing tables. In a given week, he can work no more than 14 total hours and must earn a minimum of $180. If xx represents the number of hours lifeguarding and yy represents the number of hours clearing tables, write and solve a system of inequalities graphically and determine one possible solution.

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adioabiola

The number of hours spent lifeguarding and clearing tables is 5.4 hours and 8.6 hours respectively

Solving inequality equation

  • x = number of hours lifeguarding
  • y = number of hours clearing tables

x + y ≤ 14 (1)

19x + 9y ≤ 180 (2)

From (1)

x = 14 - y

substitute into (2)

19x + 9y ≤ 180

19(14 - y) + 9y ≤ 180

266 - 19y + 9y ≤ 180

- 19y + 9y ≤ 180 - 266

- 10y ≤ -86

y ≤ -86 / -10

y ≤ 8.6 hours

  • substitute into (1)

x + y ≤ 14

x + 8.6 ≤ 14

x ≤ 14 - 8.6

x ≤ 5.4 hours

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