The Farmers Market sells apples by the bushel, and each bushel of apples weighs 42 lbs. A bushel of large apples contains 84 apples. If a bushel of small apples contains twice as many apples as a bushel of large apples, how many small apples are in 1 lb of apples?
Megan purchased a bushel of apples from the Farmers Market that contained only large and small apples. There were exactly 129 apples in the bushel Megan purchased. Based on this and information from the previous problem, what is the positive difference between the number of large apples and the number of small apples in the bushel of apples Megan purchased?
since twice as many small apples fit, 2*84=168 small apples fit in a bushel.
one way to look at it is that if each large apple is replaced by two small apples, then since 129 is 84+45, there are 45 extra apples in the basket. So, 45 of the large apples were replaced by small apples, making
84-45 = 39 large apples and
90 small apples.
164
To find out how many small apples are in 1 lb, we need to determine the number of small apples in a bushel of small apples.
Since a bushel of large apples contains 84 apples, a bushel of small apples contains twice as many, which is 84 * 2 = 168 apples.
Therefore, a bushel of small apples weighs 168 apples * (1 lb / 42 apples) = 4 lbs.
So, there are 168 small apples / 4 lbs = 42 small apples in 1 lb of apples.
Now, let's analyze Megan's purchase. We know that there were 129 apples in the bushel she bought.
Let's assume there were L large apples and S small apples in her bushel.
From the information given, we can form the following equation:
L + S = 129 (equation 1)
We also know that a bushel of large apples contains 84 apples and a bushel of small apples contains twice as many, which is 168 apples.
So, we can form another equation based on the number of large and small apples:
L + 2S = 129 (equation 2)
To find the positive difference between the number of large apples and small apples, we subtract equation 1 from equation 2:
(L + 2S) - (L + S) = 129 - 129
S = 0
This means there are no small apples in Megan's bushel.
Therefore, the positive difference between the number of large apples and small apples is L (the number of large apples) - S (the number of small apples) = L.
So the positive difference between the number of large apples and small apples in Megan's bushel of apples is L = 129.
To find the number of small apples in 1 lb of apples, we first need to determine the number of small apples in a bushel of large apples.
Given that a bushel of large apples contains 84 apples, we know that a bushel of small apples contains twice as many apples. Therefore, a bushel of small apples contains 84 * 2 = 168 apples.
Next, we can calculate the weight of a bushel of small apples. Since a bushel of large apples weighs 42 lbs, we know that a bushel of small apples would have the same weight, 42 lbs.
Now, to find the number of small apples in 1 lb of apples, we divide the total number of small apples in a bushel (168) by the weight of a bushel (42). So, there are 168 / 42 = 4 small apples in 1 lb of apples.
Moving on to the second part of the problem, let's denote the number of large apples by L and the number of small apples by S.
We know that there were exactly 129 apples in the bushel Megan purchased. So, we can write the equation L + S = 129.
From the previous problem, we found that a bushel of large apples contains 84 apples. Therefore, we can write the equation L = 84.
Substituting the value of L from the second equation into the first equation, we have 84 + S = 129.
Simplifying the equation, we find S = 129 - 84 = 45.
The positive difference between the number of large apples and the number of small apples in the bushel of apples Megan purchased is |L - S| = |84 - 45| = 39. Therefore, the positive difference is 39.