Question 1205903
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A square patchwork quilt is made of many small squares. The quilt is too small 
to place on designated furniture. Quilt is to be enlarged square one row each way. 
177 more squares are made and are just enough to increase to desired size. 
Determine number of small squares in original.
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<pre>
Let n be the number of small squares in each way, originally.


After adding one row each way, there are (n+1) small squares in each way. 


The area of the original patchwork quilt is  n^2;
The area of the patchwork quilt after enlarging is  (n+1)^2;
the difference of the two areas is 177. So, we can write this equation 

    (n+1)^2 - n^2 = 177.


Simplify this equation and find n

    n^2 + 2n + 1 - n^2 = 177

          2n + 1 = 177

          2n = 177 - 1 = 176

           n           = 176/2 = 88.


<U>ANSWER</U>.  The number of small squares originally is 88^2 = 7744.
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Solved.