Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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) 
216 r+5b=435

220 r+16 b=18.25
(B) 
216 b+5r=435

220 b+16 r=18.25
(C) 
216 r+220 b=435

5r+16 b=18.25
(D) 
216 b+220 r=435

5b+16 r=18.25

Each cup of cooked brown rice has 216216 calories and 55 grams of protein. Each cup of kidney beans has 220220 calories and 1616 grams of protein. Which of the following systems of equations could be used to determine the amount of rice, r r , in cups, and the amount of beans, b b , in cups, that should be eaten in order to consume 435435 calories and 1818.2525 grams of protein?\newlineChoose 11 answer:\newline(A) 216r+5b=435 216 r+5 b=435 \newline220r+16b=18.25 220 r+16 b=18.25 \newline(B) 216b+5r=435 216 b+5 r=435 \newline220b+16r=18.25 220 b+16 r=18.25 \newline(C) 216r+220b=435 216 r+220 b=435 \newline5r+16b=18.25 5 r+16 b=18.25 \newline(D) 216b+220r=435 216 b+220 r=435 \newline5b+16r=18.25 5 b+16 r=18.25

Full solution

Q. Each cup of cooked brown rice has 216216 calories and 55 grams of protein. Each cup of kidney beans has 220220 calories and 1616 grams of protein. Which of the following systems of equations could be used to determine the amount of rice, r r , in cups, and the amount of beans, b b , in cups, that should be eaten in order to consume 435435 calories and 1818.2525 grams of protein?\newlineChoose 11 answer:\newline(A) 216r+5b=435 216 r+5 b=435 \newline220r+16b=18.25 220 r+16 b=18.25 \newline(B) 216b+5r=435 216 b+5 r=435 \newline220b+16r=18.25 220 b+16 r=18.25 \newline(C) 216r+220b=435 216 r+220 b=435 \newline5r+16b=18.25 5 r+16 b=18.25 \newline(D) 216b+220r=435 216 b+220 r=435 \newline5b+16r=18.25 5 b+16 r=18.25
  1. Identify Variables: Identify the variables and what they represent.\newlineThe problem states that rr represents the amount of rice in cups, and bb represents the amount of beans in cups.
  2. Set Up Equations (Calories): Set up the first equation using the calorie information.\newlineEach cup of rice has 216216 calories, and each cup of beans has 220220 calories. The total calories consumed must equal 435435. This gives us the equation:\newline216r+220b=435216r + 220b = 435
  3. Set Up Equations (Protein): Set up the second equation using the protein information.\newlineEach cup of rice has 55 grams of protein, and each cup of beans has 1616 grams of protein. The total protein consumed must equal 18.2518.25 grams. This gives us the equation:\newline5r+16b=18.255r + 16b = 18.25
  4. Compare Equations: Compare the equations from Steps 22 and 33 with the answer choices.\newlineThe correct system of equations must match the equations we derived from the calorie and protein information. The equations we have are:\newline216r+220b=435216r + 220b = 435 (calories)\newline5r+16b=18.255r + 16b = 18.25 (protein)\newlineLooking at the answer choices, we see that option (C) matches our equations.

More problems from Solve linear equations with variables on both sides: word problems