A jar of jelly bean candies weighs 8 ounces. A container of caramel candies weighs 40 ounces. Lúcia buys 10 pounds worth of jelly bean candy jars and caramel candy containers for her big party. Given that there are 16 ounces in a pound, which of the following equations correctly relates the number of jars of jelly bean candies, j, and the number of containers of caramel candies, c, that Lúcia bought? Choose 1 answer: (A) (8)/(16)j+(40)/(16)c=10 (B) 8j+40 c=10 (c) (16)/(8)j+(16)/(40)c=10 (D) 16*8j+16*40 c=10

Question

A jar of jelly bean candies weighs 8 ounces. A container of caramel candies weighs 40 ounces. Lúcia buys 10 pounds worth of jelly bean candy jars and caramel candy containers for her big party. Given that there are 16 ounces in a pound, which of the following equations correctly relates the number of jars of jelly bean candies,  j, and the number of containers of caramel candies,  c, that Lúcia bought? Choose 1 answer: (A)  (8)/(16)j+(40)/(16)c=10 (B)  8j+40 c=10 (c)  (16)/(8)j+(16)/(40)c=10 (D)  16*8j+16*40 c=10

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Convert to Ounces: Convert the total weight Lúcia wants to buy from pounds to ounces. Lúcia wants to buy 10 pounds of candy. There are 16 ounces in a pound, so the total weight in ounces is: 10 pounds * 16 ounces/pound = 160 ounces.Set up Equation: Set up the equation that represents the total weight of the candies in terms of the number of jars of jelly beans (j) and the number of containers of caramel candies (c). Each jar of jelly beans weighs 8 ounces, and each container of caramel candies weighs 40 ounces. The total weight of the candies is the sum of the weight of the jelly bean jars and the caramel containers, which equals 160 ounces. So the equation is: 8 ounces/jar * j + 40 ounces/container * c = 160 ounces.Simplify Equation: Simplify the equation by dividing all terms by the common factor of 8 ounces to find the equation that relates j and c. Dividing each term by 8 ounces gives us: j + 5c = 20.Check Answer Choices: Check the answer choices to see which one matches the simplified equation. (A) (8)/(16)j + (40)/(16)c = 10 simplifies to j/2 + 5c/2 = 10, which is not the same as j + 5c = 20. (B) 8j + 40c = 10 is the original equation before converting the total weight to ounces, so it is incorrect. (C) (16)/(8)j + (16)/(40)c = 10 simplifies to 2j + 2/5c = 10, which is not the same as j + 5c = 20. (D) 16*8j + 16*40c = 10 is not correct because it does not represent the total weight in ounces. None of the answer choices match the simplified equation j + 5c = 20.Find Mistake: Realize there is a mistake in the previous steps because none of the answer choices match the correct equation. We need to go back and check our work to find the error.

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