A boat must carry aluminum pieces for a construction project that weigh, in total, no more than 50,000 kilograms (kg). Each aluminum piece is either a beam, which weighs 100kg, or a connector plate, which weighs 2kg. If the boat is carrying the maximum weight of aluminum pieces, which of the following gives the number of beams, b(c), as a function of the number of connector plates, c ? Choose 1 answer: (A) b(c)=500-0.02 c (B) b(c)=25,000-50 c (C) b(c)=50,000-100 c (D) b(c)=50,000-2c

Question

A boat must carry aluminum pieces for a construction project that weigh, in total, no more than 50,000 kilograms  (kg). Each aluminum piece is either a beam, which weighs  100kg, or a connector plate, which weighs  2kg. If the boat is carrying the maximum weight of aluminum pieces, which of the following gives the number of beams,  b(c), as a function of the number of connector plates,  c ? Choose 1 answer: (A)  b(c)=500-0.02 c (B)  b(c)=25,000-50 c (C)  b(c)=50,000-100 c (D)  b(c)=50,000-2c

Bytelearn · Accepted Answer

Understand the problem: Understand the problem. We need to find a function b(c) that gives the number of beams in terms of the number of connector plates, given that the total weight of the aluminum pieces carried by the boat cannot exceed 50,000 kg. Each beam weighs 100 kg and each connector plate weighs 2 kg.Set up the equation: Set up the equation for the total weight. Let b be the number of beams and c be the number of connector plates. The total weight of the beams and connector plates cannot exceed 50,000 kg. This can be expressed as: 100b + 2c ≤ 50,000Solve for b: Solve for b in terms of c. To find b(c), we need to express b as a function of c. We can rearrange the equation to solve for b: 100b = 50,000 - 2c b = (50,000 - 2c) / 100 b = 500 - 0.02cMatch the function: Match the function b(c) with the given options. The function we derived is b(c) = 500 - 0.02c. This matches with option (A).

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