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

Question

1
4
of the shipment by weight, how many pounds of apples are green?

Answer 1

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}.