SOLUTION: in a certain orchard there are 4 more rows of trees than there are trees in a row; & if the same number of trees were so arranged that there should be 64 added to each row,the numb

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Question 1085654: in a certain orchard there are 4 more rows of trees than there are trees in a row; & if the same number of trees were so arranged that there should be 64 added to each row,the number of the rows would be reduced to 4. how many trees are there in orchard?
Found 2 solutions by ikleyn, josmiceli:
Answer by ikleyn(52785) About Me  (Show Source):
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = the number of rows of trees
Let +b+ = the number of trees in a row
+a%2Ab+ = the total number of trees
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(1) +a+=+b+%2B+4+
(2) +%28+b+%2B+64+%29%2A4+=+a%2Ab+
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(2) +4b+%2B+256+=+a%2Ab+
(2) +4b+%2B+256+=+%28+b+%2B+4+%29%2Ab+
(2) +4b+%2B+256+=+b%5E2+%2B+4b+
(2) +b%5E2+=+256+
(2) +b+=+16+
and
(1) +a+=+b+%2B+4+
(1) +a+=+16+%2B+4+
(1) +a+=+20+
---------------------
+a%2Ab+ = the total number of trees
+a%2Ab+=+20%2A16+
+a%2Ab+=+320+
There are 320 trees in the orchard
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check:
(2) +%28+b+%2B+64+%29%2A4+=+a%2Ab+
(2) +%28+16+%2B+64+%29%2A4+=+20%2A16+
(2) +80%2A4+=+320+
(2) +320+=+320+
OK