SAT Mathematics Practice Test 5

Question : 7 of 58

Marks: +1, -0

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

$12x+9.5y ≤ 220$
$x+y ≥ 20$
$12x+9.5y ≤ 220$
$x+y ≤ 20$
$12x+9.5y ≥ 220$
$x+y ≤ 20$
$12x+9.5y ≥ 220$
$x+y ≥ 20$

Validate

Solution:

If Jackie works x hours as a tutor, which pays 12 dollars per hour, she earns

12x

dollars. If Jackie works y hours as a lifeguard, which pays 9.50 dollars per hour, she earns

9.5y

dollars. Thus the total, in dollars, Jackie earns in a week that she works x hours as a tutor and y hours as a lifeguard is

12x+9.5y.

Therefore, the condition that Jackie wants to earn at least 220 dollars is represented by the inequality

12x+9.5y ≥ 220.

The condition that Jackie can work no morethan 20 hours per week is represented by the inequality

x+y ≤ 20.

These two inequalities form the system shown in choice C.
Choice A is incorrect. This system represents the conditions that Jackie earns no more than 220 dollars and works at least 20 hours. Choice B is incorrect. The first inequality in this system represents the condition that Jackie earns no more than 220 dollars . Choice D is incorrect. The second inequality in this system represents the condition that Jackie works at least 20 hours.

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