Teddy is delivering boxes of paper to each floor of an office building. Each box weighs 56 pounds, and Teddy himself weighs 140 pounds. If the maximum capacity of an elevator is 2,000 pounds, which of the following inequalities describes the number of boxes, b, Teddy can safely take on each elevator trip without going over the capacity?Choose 1 answer:(A) b≥32(B) b≤32(C) b≥33(D) b≤33
Q. Teddy is delivering boxes of paper to each floor of an office building. Each box weighs 56 pounds, and Teddy himself weighs 140 pounds. If the maximum capacity of an elevator is 2,000 pounds, which of the following inequalities describes the number of boxes, b, Teddy can safely take on each elevator trip without going over the capacity?Choose 1 answer:(A) b≥32(B) b≤32(C) b≥33(D) b≤33
Calculating Maximum Box Capacity: We need to calculate the maximum number of boxes that can be taken on the elevator without exceeding the maximum capacity. We know the weight of each box and Teddy's weight. We will use these to form an inequality.Teddy's weight: 140 poundsWeight of each box: 56 poundsMaximum elevator capacity: 2000 poundsLet's denote the number of boxes by b.The total weight of Teddy and the boxes he carries cannot exceed the elevator's capacity.Total weight = Teddy's weight + (Weight of each box × Number of boxes)Total weight = 140+56bThe inequality that represents this situation is:140+56b≤2000
Solving the Inequality for : Now we need to solve the inequality for to find the maximum number of boxes Teddy can carry.First, we subtract Teddy's weight from both sides of the inequality:
Finding the Number of Boxes Teddy Can Carry: Next, we divide both sides of the inequality by the weight of each box to find the number of boxes:\newlineb \leq \frac{186018601860}{565656}\newlineb \leq 333333.214285721428572142857\newlineSince the number of boxes, b, must be a whole number, Teddy cannot take a fraction of a box. Therefore, we round down to the nearest whole number.\newlineb \leq 333333
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