document.write( "Question 794180: out of seven numbers, average of first six number is 40 and avarage of last six number is 35. the first number is 55. so, what is the difference between first and last number?
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Algebra.Com's Answer #480588 by DrBeeee(684)\"\" \"About 
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Let the seven numbers be represented by
\n" ); document.write( "(1) {a,b,c,d,e,f,g} and
\n" ); document.write( "let sum(b-f) be the sum of numbers b through f.
\n" ); document.write( "For the average of the first six we have
\n" ); document.write( "(2) (a + sum(b-f))/6 = 40 or
\n" ); document.write( "(3) (a + sum(b-f)) = 240
\n" ); document.write( "We are given that the first number, a, is 55, so we have
\n" ); document.write( "(4) sum(b-f)) = 240 - a or
\n" ); document.write( "(5) sum(b-f)) = 240 - 55 or
\n" ); document.write( "(6) sum(b-f)) = 185
\n" ); document.write( "Now for the average of the last six numbers we have
\n" ); document.write( "(7)(sum(b-f) + g)/6 = 35 or
\n" ); document.write( "(8)(sum(b-f) + g) = 210
\n" ); document.write( "Now use (6) in (8) to get
\n" ); document.write( "(9) 185 + g = 210 or
\n" ); document.write( "(10) g = 210 - 185 or
\n" ); document.write( "(11) g = 25
\n" ); document.write( "Answer: The first number is 55 and the last number is 25, giving an absolute difference of 30.
\n" ); document.write( "PS We have no idea what the five in between numbers are! \n" ); document.write( "
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