Jackie has two summer jobs. She works as a tutor, which pays $$ 12$ per hour, and she works as a lifeguard, which pays $$ 9.50$ per hour. She can work no more than 20 hours per week, but she wants to earn at least $$ 220$ per week. Which of the following systems of inequalities represents this situation in terms of x and y, where x is the number of hours she tutors and y is the number of hours she works as a lifeguard?

12 x + 9.5 y \leq 220; x + y \geq 20

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12 x + 9.5 y \leq 220; x + y \leq 20

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12 x + 9.5 y \geq 220; x + y \leq 20

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12 x + 9.5 y \geq 220; x + y \leq 20

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Solution

The correct option is C $12 x + 9.5 y \geq 220; x + y \leq 20$
Given that Jackie works x hours as a tutor and y hours as a lifeguard during a week. The pays for the jobs are respectively $$ 12$ per hour and $$ 9.5$ per hour. Hence, total amount earned per week is 12x + 9.5y. Totla amount to be earned is at least $$ 220$ . Therefore,
$12 x + 9.5 y \geq 220$
Further, total number of working hours is (x + y), which is capped at 20. Therefore,
$x + y \leq 20$
Hence, C is the correct choice.

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