document.write( "Question 1146604: Lee spent $1200 on holiday.Iff he had spent $50 less per day,he could have stayed an extra two days.How long was his holiday? \n" ); document.write( "

Algebra.Com's Answer #767909 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "Let x be the actual number of days of the vacation. Then

\n" ); document.write( "1200/x = daily amount spent
\n" ); document.write( "1200/(x+2) = daily amount spent if the vacation were 2 days longer

\n" ); document.write( "The amount spent per day would have been $50 less if the vacation had been 2 days longer:

\n" ); document.write( " $\"1200%2F%28x%2B2%29+=+1200%2Fx-50\"$

\n" ); document.write( "Divide by the common factor of 50 to make the numbers smaller that you have to work with:

\n" ); document.write( " $\"24%2F%28x%2B2%29+=+24%2Fx-1\"$

\n" ); document.write( "Multiply by the least common denominator, (x)(x+2):

\n" ); document.write( " $\"24x+=+24%28x%2B2%29-x%28x%2B2%29\"$
\n" ); document.write( " $\"24x+=+24x%2B48-x%5E2-2x\"$
\n" ); document.write( " $\"x%5E2%2B2x-48+=+0\"$
\n" ); document.write( " $\"%28x%2B8%29%28x-6%29+=+0\"$
\n" ); document.write( " $\"x+=+-8\"$ or $\"x+=+6\"$

\n" ); document.write( "Clearly the negative value makes no sense in the problem, so

\n" ); document.write( "ANSWER: the vacation lasted x=6 days

\n" ); document.write( "CHECK:
\n" ); document.write( "1200/6 = 200
\n" ); document.write( "1200/8 = 150
\n" ); document.write( "200-150 = 50 \n" ); document.write( "

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