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Question 209624: The Orchard brothers always plant their apple trees in square arrays, like those illustrated. This year they planted 29 more apple trees in their square orchard than last year. If the orchard is still square, how many apple trees are there in the orchard this year?
Found 3 solutions by kensson, Alan3354, ankor@dixie-net.com:
Answer by kensson(21)   (Show Source):
You can put this solution on YOUR website! So, we've got two squares with whole-number sides, and the difference between their areas is 29.
We know that the difference of two squares is  , so we need to figure out what multiplies to make 29... and we know 29 is prime, so the factors must be 1 and 29.
Since x and y are both positive, they have to add up to more than their difference, so we get
1) x + y = 29
2) x - y = 1
We can solve that several ways, all of which give us x = 15 (this year's crop) and y = 14 (last year's). This year there are  trees; last year there were 196.
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! 29/2 = 14.5 --> 14 and 15
There are now 225 trees (15 by 15).
Last year they had 196 (14 by 14).
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Don't waste time (especially on a test) doing these the hard way.
Answer by ankor@dixie-net.com(22740)  (Show Source):
You can put this solution on YOUR website! The Orchard brothers always plant their apple trees in square arrays, like those illustrated.
This year they planted 29 more apple trees in their square orchard than last year.
If the orchard is still square, how many apple trees are there in the orchard this year?
:
If you add 29 trees and still maintain a square, you add 15 to one side and 14
to the adjacent side; a square would be: 15^2 = 225 trees this year
;
:
Check by finding last years trees: 225 - 29 = 196; which is 14^2
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