Question

a=3t a+t=60 The given system of equations describes a, the number of hours Austin works each week, and t, the number of hours Tori works each week. Which of the following best interprets the number 3 in the system? A. Tori works 3 times as many hours each week as Austin does. B. Austin works 3 times as many hours each week as Tori does. C. Austin works 3 more hours each week than Tori does. D. Tori works 3 hours each week.

Answer 1

The number 3 in the equation a = 3t means that Austin works three times as many hours as Tori does each week, making option B the correct interpretation.

Step-by-step explanation:

The student is presented with a system of equations representing the number of hours Austin (a) and Tori (t) work each week:

• a = 3t

• a + t = 60

The number 3 in the equation a = 3t signifies that Austin works three times as many hours as Tori does each week. Therefore, the correct interpretation of the number 3 is:

B. Austin works 3 times as many hours each week as Tori does.

To understand why option B is correct, realize that the equation a = 3t can also be read as 'Austin's hours (a) are equal to three times Tori's hours (t).' Meanwhile, the equation a + t = 60 signifies that the total number of hours worked by both together is 60. This does not indicate anything about the individual ratio of their working hours.