document.write( "Question 1011602: The sum of two distinct numbers is 26. If the smaller number is reduced by 1 and the larger number by 3, the product of the two resulting number is 120. What are the numbers? \n" ); document.write( "
Algebra.Com's Answer #627345 by addingup(3677)\"\" \"About 
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x+y= 26 so if we want y only we can subtract x from 26:
\n" ); document.write( "y= 26-x Remember this value for y
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\n" ); document.write( "(x-1)(y-3)= 120 Let's substitute for y:
\n" ); document.write( "(x-1)(26-x-3)= 120
\n" ); document.write( "(x-1)(23-x)= 120
\n" ); document.write( "Do FOIL on this equation:
\n" ); document.write( "23x+-x^2+-23+x= 120 Simplify and re-arrange:
\n" ); document.write( "-x^2+24x-23= 120 Multiply both sides by -1
\n" ); document.write( "x^2-24x+23= -120 Add 120 on both sides
\n" ); document.write( "x^2-24x+143= 0 Factor this equation (FOIL) and you get:
\n" ); document.write( "(x-13)(x-11)= 0 Split into 2 equations:
\n" ); document.write( "x-13=0 or x-11= 0
\n" ); document.write( "x= 13 or x= 11
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\n" ); document.write( "Let's try these numbers and see which one is correct:
\n" ); document.write( "(13-1)(y-3)= 120 solve for y:
\n" ); document.write( "y= 13 This is not our answer, the problem clearly states \"two distinct numbers\" and \"smaller number\", \"larger number\".
\n" ); document.write( "Let's try 11:
\n" ); document.write( "(11-1)(y-3)= 120
\n" ); document.write( "y= 15 Now we have an answer:
\n" ); document.write( "11-1*15-3= 120
\n" ); document.write( "10*12= 120
\n" ); document.write( "120= 120 We've got the correc answer \n" ); document.write( "
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