document.write( "Question 95253: If the length of a rectangle is decreased by 2 inches and its width is increased by 2 inches, the area of the rectangle increases by 16 square inches. If the length is increased by 5 inches and the width is decreased by 3 inches, the area of the rectangle increases by 15 square inches. What is the area of the original rectangle? \n" ); document.write( "
Algebra.Com's Answer #69340 by ankor@dixie-net.com(22740)\"\" \"About 
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If the length of a rectangle is decreased by 2 inches and its width is increased by 2 inches, the area of the rectangle increases by 16 square inches. If the length is increased by 5 inches and the width is decreased by 3 inches, the area of the rectangle increases by 15 square inches. What is the area of the original rectangle?
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\n" ); document.write( "Let x = length, and y = width of the original rectangle
\n" ); document.write( "x*y = area of original rectangle
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\n" ); document.write( "1st rectangle equation from the statement:
\n" ); document.write( "\"If the length of a rectangle is decreased by 2 inches and its width is increased by 2 inches, the area of the rectangle increases by 16 square inches.
\n" ); document.write( "(x-2)*(y+2) = xy + 16
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\n" ); document.write( "xy + 2x - 2y - 4 = xy + 16; FOILed (x-2)*(y+2)
\n" ); document.write( "xy - xy + 2x - 2y = 16 + 4; arrange the unknowns on the left, numbers on right
\n" ); document.write( "2x - 2y = 20
\n" ); document.write( "x - y = 10; simplified, divided by 2
\n" ); document.write( "x = (y + 10)
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\n" ); document.write( "1nd rectangle equation from the statement:
\n" ); document.write( "\" If the length is increased by 5 inches and the width is decreased by 3 inches, the area of the rectangle increases by 15 square inches.\"
\n" ); document.write( "(x+5)*(y-3) = xy + 15
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\n" ); document.write( "xy - 3x + 5y - 15 = xy + 15
\n" ); document.write( "xy - xy - 3x + 5y = 15 + 15
\n" ); document.write( "-3x + 5y = 30
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\n" ); document.write( "Substitute (y+10) for x from the 1st equation:
\n" ); document.write( "-3(y+10) + 5y = 30
\n" ); document.write( "-3y - 30 + 5y = 30
\n" ); document.write( "-3y + 5y = 30 + 30
\n" ); document.write( "2y = 60
\n" ); document.write( "y = 30 inches, width of the original square
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\n" ); document.write( "Find x:
\n" ); document.write( "x = y + 10
\n" ); document.write( "x = 40 inches, length of the original square
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\n" ); document.write( "What is the area of the original rectangle?
\n" ); document.write( "40 * 30 = 1200 sq inches
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\n" ); document.write( "Check solutions using the changed rectangles
\n" ); document.write( "1st rectangle: 38 * 32 = 1216 sq inches
\n" ); document.write( "2nt rectangle: 45 * 27 = 1215 sq inches
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\n" ); document.write( "Did this make sense to you? Any questions? \n" ); document.write( "
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