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) 30h+140p≤400(B) 30h+140p≥400(C) 140h+30p≤400(D) 140h+30p≥400
Q. 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) 30h+140p≤400(B) 30h+140p≥400(C) 140h+30p≤400(D) 140h+30p≥400
Define Variables: Let's define the variables:h= the number of 140-pound humansp= the number of 30-pound packsThe maximum carrying capacity of the camel is 400 pounds.We need to find an inequality that represents the total weight of humans and packs that the camel can carry without exceeding its maximum capacity.
Write Total Weight Equation: We can write an equation for the total weight that the camel is carrying:Total weight = (weight per human ∗ number of humans) + (weight per pack ∗ number of packs)Total weight = 140h+30pSince the camel cannot carry more than its maximum capacity, the total weight must be less than or equal to400 pounds.So, the inequality should be:140h+30p≤400
Create Inequality: Now, let's check the given options to see which one matches our inequality:(A) 30h+140p≤400 (This is incorrect because it swaps the weights of humans and packs.)(B) 30h+140p≥400 (This is incorrect because it swaps the weights and suggests the camel can carry at least 400 pounds, which is not the maximum limit.)(C) 140h+30p≤400 (This is correct as it matches our inequality.)(D) 140h+30p≥400 (This is incorrect because it suggests the camel can carry at least 400 pounds, which is not the maximum limit.)
More problems from Write a linear inequality: word problems