document.write( "Question 898326: find two consecutive integers such that the sum of one third of the first integer and one fourth of the second integer is 9. \n" ); document.write( "

Algebra.Com's Answer #544757 by KMST(5328) $\"\"$ $\"About$

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THE ALGEBRA WAY:
\n" ); document.write( " $\"n\"$ = the smaller of the two consecutive integers
\n" ); document.write( " $\"n%2B1\"$ = the largerer of the two consecutive integers
\n" ); document.write( "The problem says that
\n" ); document.write( " $\"n%2F3%2B%28n%2B1%29%2F4=9\"$
\n" ); document.write( "Multiplying both sides of the equalsign times $\"3%2A4=12\"$ we get
\n" ); document.write( " $\"12%28n%2F3%2B%28n%2B1%29%2F4%29=12%2A9\"$
\n" ); document.write( " $\"12%2An%2F3%2B12%28n%2B1%29%2F4=108\"$
\n" ); document.write( " $\"4n%2B3%28n%2B1%29=108\"$
\n" ); document.write( " $\"4n%2B3n%2B3=108\"$
\n" ); document.write( " $\"7n%2B3=108\"$
\n" ); document.write( " $\"7n=108-3\"$
\n" ); document.write( " $\"7n=105\"$
\n" ); document.write( " $\"n=105%2F7\"$
\n" ); document.write( " $\"highlight%28n=15%29\"$
\n" ); document.write( "The two consecutive integers are $\"highlight%2815%29\"$ and $\"highlight%2816%29\"$ .
\n" ); document.write( "
\n" ); document.write( "ANOTHER WAY (Guess and check):
\n" ); document.write( "One third of the first integer must be an integer (a whole number),
\n" ); document.write( "and one fourth of the second integer must be an integer too.
\n" ); document.write( "Otherwise, one or both would be fractions that would add up to a fraction.
\n" ); document.write( "The first integer could be 0, 3, 6, 9, 12, 15, 18, 21, 24, ....,
\n" ); document.write( "and one third of that would be 0, 1, 2, 3, 4, 5, 6, 7, 8, ....
\n" ); document.write( "If we add 1 to each of those choices, the second integer would be 1, 4, 7, 13, 16, 19, 22, 25, ...., but not all of those numbers divide by 4 evenly.
\n" ); document.write( "Only 4, and 16 do.
\n" ); document.write( "If the second integer were 4 and the first one were 3,
\n" ); document.write( "one third of the first integer and one fourth of the second integer would be
\n" ); document.write( " $\"3%2F3%2B4%2F4=1%2B1=2\"$ , so 3 and 4 is not the answer.
\n" ); document.write( "If the second integer were 16 and the first one were 15,
\n" ); document.write( "one third of the first integer and one fourth of the second integer would be
\n" ); document.write( " $\"15%2F3%2B16%2F4=5%2B4=9\"$ , so $\"highlight%2815%29\"$ and $\"highlight%2816%29\"$ is the answer. \n" ); document.write( "

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