A company produces candy bags that each hold about 528 cubic inches of candy. Each bag is filled with any mixture of lollipop candies and gummy bear candies. When a bag contains only lollipop candies, then it has about 361 candies. When a bag contains only gummy bear candies, then it has about 697 candies. Given any candy bag produced by this company, which of the following equations could relate the approximate number of lollipop candies, l, in the bag and the approximate number of gummy bear candies, g, in the bag? Choose 1 answer: (A) (l)/( 361)+(g)/( 697)=528 (B) 361 l+697 g=528 (C) (l)/( 361)+(g)/( 697)=1 (D) 361 l+697 g=1

Question

A company produces candy bags that each hold about 528 cubic inches of candy. Each bag is filled with any mixture of lollipop candies and gummy bear candies. When a bag contains only lollipop candies, then it has about 361 candies. When a bag contains only gummy bear candies, then it has about 697 candies. Given any candy bag produced by this company, which of the following equations could relate the approximate number of lollipop candies,  l, in the bag and the approximate number of gummy bear candies,  g, in the bag? Choose 1 answer: (A)  (l)/( 361)+(g)/( 697)=528 (B)  361 l+697 g=528 (C)  (l)/( 361)+(g)/( 697)=1 (D)  361 l+697 g=1

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Understand Problem: Understand the problem and what is being asked. We need to find an equation that relates the number of lollipop candies (l) and gummy bear candies (g) in a bag that holds 528 cubic inches of candy. We know the number of candies when the bag is filled with only one type of candy.Determine Relationship: Determine the relationship between the number of candies and the volume of the bag. The volume of the bag is constant at 528 cubic inches. When filled with only lollipops, it holds 361 candies, and when filled with only gummy bears, it holds 697 candies. This suggests that the volume of each type of candy is proportional to the number of candies.Formulate Equation: Formulate the equation based on the given information. We can assume that each lollipop takes up a certain volume, and each gummy bear takes up a certain volume. The total volume of lollipops and gummy bears together should equal the total volume of the bag. Therefore, we can write the equation as a sum of the volumes of lollipops and gummy bears, which should equal the total volume of the bag.Express Volumes: Express the volume of lollipops and gummy bears in terms of l and g. If we assume that each lollipop takes up 1/361 of the bag's volume and each gummy bear takes up 1/697 of the bag's volume, then the volume taken up by l lollipops and g gummy bears can be expressed as (l/361) + (g/697).Set Equal to Total Volume: Set the sum of the volumes equal to the total volume of the bag. The total volume of the bag is 528 cubic inches, but since we are looking for a proportion, we want the sum of the volumes to equal 1 (as in, the bag is 100% full). Therefore, the equation should be (l/361) + (g/697) = 1.Choose Correct Answer: Choose the correct answer from the given options. Based on our previous steps, the correct equation that relates the number of lollipop candies (l) and gummy bear candies (g) in the bag is (l/361) + (g/697) = 1. This corresponds to option (C).

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