Select the correct answerFive farmers have 7,9,11,13 & 14 apple trees respectively in their orchards. Last year each of them discovered that every tree in their own orchard yields exactly the same number of apples. Further, if the 3rd farmer gives one apple to the 1st and the 5th gives 3 to each of the 2nd & d 4th, they would all exactly have the same number of apples, what were the yields per tree in the orchards of the 3rd & 4th farmers ?Options 9 & 9 9 & 1117 & 9 11 & 9
Question
Select the correct answerFive farmers have 7,9,11,13 & 14 apple trees respectively in their orchards. Last year each of them discovered that every tree in their own orchard yields exactly the same number of apples. Further, if the 3rd farmer gives one apple to the 1st and the 5th gives 3 to each of the 2nd & d 4th, they would all exactly have the same number of apples, what were the yields per tree in the orchards of the 3rd & 4th farmers ?Options 9 & 9 9 & 1117 & 9 11 & 9
Solution
The question is asking for the number of apples each tree yields in the orchards of the 3rd and 4th farmers.
Let's denote the yield per tree for each farmer as follows: 1st farmer: a 2nd farmer: b 3rd farmer: c 4th farmer: d 5th farmer: e
From the problem, we know that the total number of apples for each farmer is the product of the number of trees and the yield per tree. So we have:
7a (1st farmer) 9b (2nd farmer) 11c (3rd farmer) 13d (4th farmer) 14e (5th farmer)
We also know that if the 3rd farmer gives one apple to the 1st and the 5th gives 3 to each of the 2nd & 4th, they would all exactly have the same number of apples. This gives us the following equations:
7a + 1 = 11c - 1 (1st and 3rd farmers) 9b + 3 = 14e - 3 (2nd and 5th farmers) 13d + 3 = 14e - 3 (4th and 5th farmers)
Solving these equations, we find that the only possible solution that fits the given options is c = 11 (yield per tree for the 3rd farmer) and d = 9 (yield per tree for the 4th farmer).
So, the correct answer is 11 & 9.
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