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Question 1107440: I grow two kinds of apples on my apple farm. One day it was time to load the apples in my
truck. By lunch time I had finished loading the McIntosh apples and started loading Gala
apples. I noticed that I had three bushels of Galas, and that one quarter of the apples in my
truck were Galas. After lunch, I finished loading the Galas. At the completion of loading
three-quarters of the apples were Galas.
In total, how many bushels of apples did I load that day?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! x = number of bushels of macintosh.
y = number of bushels of gala.
you loaded all the macintosh apples first.
that would be x bushels of macintosh.
By lunch time you had finished loading the McIntosh apples and started loading Gala
apples. you noticed that you had three bushels of Galas, and that one quarter of the apples in your truck were Galas.
since you had already loaded x bushels of macintosh and you had also loaded 3 bushels of gala, then you had a total of x + 3 bushels of apples in the truck.
1/4 of the apples in the truck were gala.
your equation for this is that 3 = 1/4 * (x + 3)
multiply both sides of this equation by 4 to get 12 = x + 3.
subtract 3 from both sides of this equation and solve for x to get x = 9.
you loaded 9 bushels of macintosh and 3 bushels of gala by lunch time.
After lunch, you finished loading the Galas. At the completion of loading
three-quarters of the apples were Galas.
the equation for this is that y = 3/4 * (x + y).
since x = 9, this equation becomes y = 3/4 * (9 + y).
multiply both sides of this equation by 4 to get 4y = 3 * (9 + y).
simplify this equation to get 4y = 27 + 3y.
subtract 3y from both sides of this equation and solve for y to get y = 27.
you loaded 9 bushels of macintosh and 27 bushels of gala for a total of 36 bushels of apples.
to confirm that you calculated correctly, go back to your original problem statements knowing what you know now and see if those original statements are true.
by lunch time you had loaded all of the macintosh and 3 of the gala.
this would be 9 bushels of macintosh and 3 bushels of gala for a total of 12 bushels.
the gala were 1/4 of the total apples loaded by lunch time.
3 / 12 = 1/4 so this statement is true.
when you were done, 3/4 of the bushels loaded were gala.
9 bushels of macintosh and 27 bushels of galas equals 36 bushels total.
27/36 = 3/4 so this statement is also true.
your solution is that you loaded 9 bushels of macintosh apples that day.
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