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 bought from pounds to ounces. Lúcia bought 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.Equation setup: Set up the equation to represent the total weight of the candies in terms of the number of jars and containers. The weight of j jars of jelly bean candies is 8 ounces per jar, so the total weight for the jelly beans is 8j ounces. The weight of c containers of caramel candies is 40 ounces per container, so the total weight for the caramels is 40c ounces. The total weight of the candies is the sum of the weights of the jelly beans and caramels, which equals 160 ounces (from Step 1). So, the equation is 8j + 40c = 160.Simplify equation: Simplify the equation if necessary. The equation 8j + 40c = 160 can be divided by 8 to simplify it: (8j + 40c) / 8 = 160 / 8 j + 5c = 20 However, this simplified equation is not one of the answer choices, so we need to check the original equation against the answer choices.Compare with choices: Compare the original equation to the answer choices. The original equation from Step 2 is 8j + 40c = 160. Let's compare this to the answer choices: (A) (8/16)j + (40/16)c = 10 simplifies to 0.5j + 2.5c = 10, which is not equivalent to our equation. (B) 8j + 40c = 10 is not correct because it does not account for the total weight of 160 ounces. (C) (16/8)j + (16/40)c = 10 simplifies to 2j + 0.4c = 10, which is not equivalent to our equation. (D) 16*8j + 16*40c = 10 is not correct because it would greatly exceed the total weight of 160 ounces. None of the answer choices match our equation, which suggests there might be a mistake in the problem or the answer choices provided.

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