Joy is loading up a cargo truck with a shipment of small and large boxes. Each small box weighs 30 pounds, and each large box weighs 75 pounds. The truck can carry at most 1,500 pounds, and Joy wants the shipment to have at least 40 boxes.
Which pairs (s,𝓁) represent possible numbers of small and large boxes Joy could ship?
a) (42, 3.2)
b) (0,20)
c) (55, -2)
d) (48, 0)
Let's denote the number of small boxes as s and the number of large boxes as l.
Since each small box weighs 30 pounds and each large box weighs 75 pounds, the total weight of the shipment can be determined by the equation:
30s + 75l ≤ 1500
We also want the shipment to have at least 40 boxes, so s + l ≥ 40
Let's go through each pair to see if they satisfy the conditions:
a) (42, 3.2):
30(42) + 75(3.2) = 1260 + 240 = 1500 (satisfies weight limit)
42 + 3.2 = 45.2 ≥ 40 (satisfies number of boxes)
Thus, (42, 3.2) is a possible pair.
b) (0, 20):
30(0) + 75(20) = 0 + 1500 = 1500 (satisfies weight limit)
0 + 20 = 20 < 40 (does not satisfy number of boxes)
Thus, (0, 20) is not a possible pair.
c) (55, -2):
30(55) + 75(-2) = 1650 - 150 = 1500 (satisfies weight limit)
55 + (-2) = 53 ≥ 40 (satisfies number of boxes)
Thus, (55, -2) is a possible pair.
d) (48, 0):
30(48) + 75(0) = 1440 + 0 = 1440 < 1500 (does not satisfy weight limit)
48 + 0 = 48 < 40 (does not satisfy number of boxes)
Thus, (48, 0) is not a possible pair.
Therefore, the possible pairs of small and large boxes that Joy could ship are:
a) (42, 3.2)
c) (55, -2)