Ellie works in the produce section at a grocery store. The store receives a shipment of green and red apples that weighs 20.4 pounds in total. Ellie separates the green and red apples into bins by color. If red apples make up
1
4
of the shipment by weight, how many pounds of apples are green?
Let G be the weight of the green apples and R be the weight of the red apples. We know that G + R = 20.4 and R = 1/4 * (G + R).
Substituting the second equation into the first equation, we get G + 1/4 * (G + R) = 20.4
Combining like terms, we get G + 1/4 * G + 1/4 * R = 20.4
Combining like terms, we get 5/4 * G + 1/4 * R = 20.4
Substituting the expression for R from the second equation into the third equation, we get 5/4 * G + 1/4 * (G + R) = 20.4
Combining like terms, we get 5/4 * G + 1/4 * G + 1/4 * R = 20.4
Combining like terms, we get 6/4 * G + 1/4 * R = 20.4
Substituting the expression for R from the second equation into the fourth equation, we get 6/4 * G + 1/4 * R = 20.4
Combining like terms, we get 6/4 * G + 1/4 * (G + R) = 20.4
Combining like terms, we get 6/4 * G + 1/4 * (G + R) = 20.4
Combining like terms, we get 6/4 * G + 1/4 * G + 1/4 * R = 20.4
Combining like terms, we get 7/4 * G + 1/4 * R = 20.4
Subtracting 1/4 * R from both sides, we get 7/4 * G = 20.4 - 1/4 * R
Dividing both sides by 7/4, we get G = (20.4 - 1/4 * R) / (7/4)
Dividing both sides by 1/4, we get G = (20.4 - 1/4 * R) / (7/4) * (4/1)
Simplifying the right side, we get G = (20.4 * 4 - 1 * R) / 7
Simplifying the right side, we get G = (81.6 - R) / 7
To find R, we can substitute this expression into the second equation: R = 1/4 * (G + R)
Substituting the expression for G, we get R = 1/4 * ((81.6 - R) / 7 + R)
Simplifying the expression inside the parentheses, we get R = 1/4 * (81.6 / 7 - R / 7 + R)
Simplifying the expression inside the parentheses, we get R = 1/4 * (11.657142857142857 - R / 7 + R)
Simplifying the expression, we get R = (11.657142857142857 - R / 7 + R) / 4
Simplifying the expression, we get R = (11.657142857142857 + 6/7 * R) / 4
Multiplying both sides by 4, we get 4 * R = 11.657142857142857 + 6/7 * R
Subtracting 6/7 * R from both sides, we get 4/7 * R = 11.657142857142857
Dividing both sides by 4/7, we get R = 11.657142857142857 / (4/7)
Multiplying both sides by 7/4, we get R = 11.657142857142857 * (7/4)
Simplifying the right side, we get R = 11.657142857142857 * 7/4
Multiplying both sides, we get R = 20.4
Plugging that back into the first equation, we get G + 20.4 = 20.4
Simplifying that, we get G = 20.4 - 20.4 = 0. Answer: \boxed{0}.
To find out how many pounds of apples are green, we need to determine the weight of the red apples first.
Given that the red apples make up 1/4 of the shipment by weight, we can calculate the weight of the red apples using the total weight of the shipment:
Weight of red apples = (1/4) * Total weight
Weight of red apples = (1/4) * 20.4 pounds
Weight of red apples = 5.1 pounds
Since the total weight of the shipment is 20.4 pounds, and the weight of the red apples is 5.1 pounds, we can find the weight of the green apples by subtracting the weight of the red apples from the total weight:
Weight of green apples = Total weight - Weight of red apples
Weight of green apples = 20.4 pounds - 5.1 pounds
Weight of green apples = 15.3 pounds
Therefore, the weight of the green apples is 15.3 pounds.