document.write( "Question 974053: The average of a list of integers goes up by 2 when 21 is added to the list. If 7 is added to the new list, then the average reduces by 1. How many numbers were there in the original list? \n" ); document.write( "
Algebra.Com's Answer #596072 by rothauserc(4718)\"\" \"About 
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x/n = y, where x is the total of integers, n is the number of integers, y is their average, then
\n" ); document.write( "(x+21) / (n+1) = (y+2)
\n" ); document.write( "(x+21+7) / (n+2) = (y+2-1)
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\n" ); document.write( "substitute ny for x and we get
\n" ); document.write( "(ny+21) = (n+1)(y+2)
\n" ); document.write( "(ny+28) = (n+2)(y+1)
\n" ); document.write( "we now have two equations in two unknowns
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\n" ); document.write( "solve first equation for y
\n" ); document.write( "ny+21 = ny+y+2n+2
\n" ); document.write( "y +2n = 19
\n" ); document.write( "y = 19-2n
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\n" ); document.write( "reduce second equation and then substitute 19-2n for y
\n" ); document.write( "ny+28 = ny+2y+n+2
\n" ); document.write( "2y+n = 26
\n" ); document.write( "substitute for y
\n" ); document.write( "2(19-2n)+n = 26
\n" ); document.write( "38-4n+n = 26
\n" ); document.write( "-3n = -12
\n" ); document.write( "n = 4, therefore
\n" ); document.write( "There are 4 numbers in the original list\r
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