document.write( "Question 87522: Two farmers always plant thier mango trees in square arrays.This year they planted 11 more mango trees in thier square,how many mango trees are there in the garden this year? \n" ); document.write( "

Algebra.Com's Answer #63454 by kev82(151) $\"\"$ $\"About$

You can put this solution on YOUR website!
Hi,
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\n" ); document.write( "\n" ); document.write( "If last year, the width of the garden was $\"x\"$ , then there would be $\"x%5E2\"$ trees. If the garden is $\"a\"$ units wider this year, then there are $\"%28x%2Ba%29%5E2\"$ trees this year. The difference between this year and last year is 11 trees. So $\"%28x%2Ba%29%5E2-x%5E2=11\"$ . If we expand that:
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\n" ); document.write( "\n" ); document.write( " $\"2xa%2Ba%5E2=11\"$ \r
\n" ); document.write( "\n" ); document.write( "Now, we had some trees last year so we know $\"x%3E0\"$ and we have more trees this year so $\"a%3E0\"$ . Also the number of trees is integer, so both $\"x\"$ and $\"a\"$ must be integers (this is easy to prove).
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\n" ); document.write( "\n" ); document.write( "Now looking at the equation, we can see that $\"a%3C4\"$ this is because a value of 4 or greater would force $\"x\"$ to be negative so a can only be 1, 2, or 3.
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\n" ); document.write( "\n" ); document.write( "If a is 1, x is 5, if a is 2, x is 7/4, and if a is 3, x is 1/3. The only integer solution here is (1,5). Which gives a crop size (number of trees) this year of (1+5)*(1+5)=36
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\n" ); document.write( "\n" ); document.write( "Hope that helps,
\n" ); document.write( "Kev \n" ); document.write( "

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