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The maximum carrying capacity of a camel is 400 pounds. Which of the following inequalities correctly models 
h, the number of 140 pound humans, and 
p, the number of 30 -pound packs the camel can carry?
Choose 1 answer:
(A) 
30 h+140 p <= 400
(B) 
30 h+140 p >= 400
(C) 
140 h+30 p <= 400
(D) 
140 h+30 p >= 400

The maximum carrying capacity of a camel is 400400 pounds. Which of the following inequalities correctly models h h , the number of 140140 pound humans, and p p , the number of 3030 -pound packs the camel can carry?\newlineChoose 11 answer:\newline(A) 30h+140p400 30 h+140 p \leq 400 \newline(B) 30h+140p400 30 h+140 p \geq 400 \newline(C) 140h+30p400 140 h+30 p \leq 400 \newline(D) 140h+30p400 140 h+30 p \geq 400

Full solution

Q. The maximum carrying capacity of a camel is 400400 pounds. Which of the following inequalities correctly models h h , the number of 140140 pound humans, and p p , the number of 3030 -pound packs the camel can carry?\newlineChoose 11 answer:\newline(A) 30h+140p400 30 h+140 p \leq 400 \newline(B) 30h+140p400 30 h+140 p \geq 400 \newline(C) 140h+30p400 140 h+30 p \leq 400 \newline(D) 140h+30p400 140 h+30 p \geq 400
  1. Define Variables: Let's define the variables:\newlineh=h = the number of 140140-pound humans\newlinep=p = the number of 3030-pound packs\newlineThe maximum carrying capacity of the camel is 400400 pounds.\newlineWe need to find an inequality that represents the total weight of humans and packs that the camel can carry without exceeding its maximum capacity.
  2. Write Total Weight Equation: We can write an equation for the total weight that the camel is carrying:\newlineTotal weight = (weight per human * number of humans) + (weight per pack * number of packs)\newlineTotal weight = 140h+30p140h + 30p\newlineSince the camel cannot carry more than its maximum capacity, the total weight must be less than or equal to 400400 pounds.\newlineSo, the inequality should be:\newline140h+30p400140h + 30p \leq 400
  3. Create Inequality: Now, let's check the given options to see which one matches our inequality:\newline(A) 30h+140p40030h + 140p \leq 400 (This is incorrect because it swaps the weights of humans and packs.)\newline(B) 30h+140p40030h + 140p \geq 400 (This is incorrect because it swaps the weights and suggests the camel can carry at least 400400 pounds, which is not the maximum limit.)\newline(C) 140h+30p400140h + 30p \leq 400 (This is correct as it matches our inequality.)\newline(D) 140h+30p400140h + 30p \geq 400 (This is incorrect because it suggests the camel can carry at least 400400 pounds, which is not the maximum limit.)

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