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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

Teddy is delivering boxes of paper to each floor of an office building. Each box weighs 5656 pounds, and Teddy himself weighs 140140 pounds. If the maximum capacity of an elevator is 22,000000 pounds, which of the following inequalities describes the number of boxes, b b , Teddy can safely take on each elevator trip without going over the capacity?\newlineChoose 11 answer:\newline(A) b32 b \geq 32 \newline(B) b32 b \leq 32 \newline(C) b33 b \geq 33 \newline(D) b33 b \leq 33

Full solution

Q. Teddy is delivering boxes of paper to each floor of an office building. Each box weighs 5656 pounds, and Teddy himself weighs 140140 pounds. If the maximum capacity of an elevator is 22,000000 pounds, which of the following inequalities describes the number of boxes, b b , Teddy can safely take on each elevator trip without going over the capacity?\newlineChoose 11 answer:\newline(A) b32 b \geq 32 \newline(B) b32 b \leq 32 \newline(C) b33 b \geq 33 \newline(D) b33 b \leq 33
  1. 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.\newlineTeddy's weight: 140140 pounds\newlineWeight of each box: 5656 pounds\newlineMaximum elevator capacity: 20002000 pounds\newlineLet's denote the number of boxes by bb.\newlineThe total weight of Teddy and the boxes he carries cannot exceed the elevator's capacity.\newlineTotal weight = Teddy's weight + (Weight of each box ×\times Number of boxes)\newlineTotal weight = 140+56b140 + 56b\newlineThe inequality that represents this situation is:\newline140+56b2000140 + 56b \leq 2000
  2. Solving the Inequality for b: Now we need to solve the inequality for b to find the maximum number of boxes Teddy can carry.\newlineFirst, we subtract Teddy's weight from both sides of the inequality:\newline5656b \leq 20002000 - 140140\newline5656b \leq 18601860
  3. 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{18601860}{5656}\newlineb \leq 3333.21428572142857\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 3333

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