Each cup of cooked brown rice has 216 calories and 5 grams of protein. Each cup of kidney beans has 220 calories and 16 grams of protein. Which of the following systems of equations could be used to determine the amount of rice, r, in cups, and the amount of beans, b, in cups, that should be eaten in order to consume 435 calories and 18.25 grams of protein?Choose 1 answer:(A) 216r+5b=435220r+16b=18.25(B) 216b+5r=435220b+16r=18.25(C) 216r+220b=4355r+16b=18.25(D) 216b+220r=4355b+16r=18.25
Q. Each cup of cooked brown rice has 216 calories and 5 grams of protein. Each cup of kidney beans has 220 calories and 16 grams of protein. Which of the following systems of equations could be used to determine the amount of rice, r, in cups, and the amount of beans, b, in cups, that should be eaten in order to consume 435 calories and 18.25 grams of protein?Choose 1 answer:(A) 216r+5b=435220r+16b=18.25(B) 216b+5r=435220b+16r=18.25(C) 216r+220b=4355r+16b=18.25(D) 216b+220r=4355b+16r=18.25
Identify Variables: Identify the variables and what they represent.The problem states that r represents the amount of rice in cups, and b represents the amount of beans in cups.
Set Up Equations (Calories): Set up the first equation using the calorie information.Each cup of rice has 216 calories, and each cup of beans has 220 calories. The total calories consumed must equal 435. This gives us the equation:216r+220b=435
Set Up Equations (Protein): Set up the second equation using the protein information.Each cup of rice has 5 grams of protein, and each cup of beans has 16 grams of protein. The total protein consumed must equal 18.25 grams. This gives us the equation:5r+16b=18.25
Compare Equations: Compare the equations from Steps 2 and 3 with the answer choices.The correct system of equations must match the equations we derived from the calorie and protein information. The equations we have are:216r+220b=435 (calories)5r+16b=18.25 (protein)Looking at the answer choices, we see that option (C) matches our equations.
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