A Michigan orchard made 14,757lb of taffy apples wih aproximately 1 lb of taffy mixtures for each 67.1 pounds of apples. TO the nearest tenth of a pound, how many pounds of apples and how many pounds of taffy were used?
Use the method decribed in your later post.
To find the number of pounds of apples and taffy used, we need to set up a proportion based on the given ratio of 1 lb of taffy mixture for each 67.1 pounds of apples.
Let's assume:
x = pounds of apples used
y = pounds of taffy used
Based on the given ratio, the proportion becomes:
1 lb taffy / 67.1 lb apples = y lb taffy / x lb apples
Now, we can set up the equation using the given information that the orchard made 14,757 lb of taffy apples:
1 / 67.1 = y / x (equation 1)
x + y = 14,757 (equation 2)
We have two equations with two unknowns (x and y), so we can solve this system of equations.
From equation 2, we can solve for y:
y = 14,757 - x
Substituting this into equation 1, we get:
1 / 67.1 = (14,757 - x) / x
Now, we can solve for x using cross multiplication:
x = (67.1 * 14,757) / (1 + 67.1)
x ≈ 9949.5910 lb
Similarly, we can find y by substituting the value of x:
y = 14,757 - x
y ≈ 14,757 - 9949.5910
y ≈ 5807.4089 lb
To the nearest tenth of a pound, the orchard used approximately 9949.6 pounds of apples and 5807.4 pounds of taffy.