document.write( "Question 785464: Find two consecutive odd integers such that three-fourths of the larger number is 5 more than one-fourth of the smaller number. Find the numbers. \n" ); document.write( "

Algebra.Com's Answer #477758 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
I do not care that if two numbers in a problem are both odd or both even. Either way the difference between the numbers would be 2.
\n" ); document.write( "I just find pairs of numbers, both odd or both even, that satisfy the conditions of the problem.
\n" ); document.write( "If the solution found does not match the parity (odd or even) required by the problem, then there is no solution to the problem. (That could happen in a real life problem, but math class problems bear little resemblance to real life, so if I find only even solutions here I will recheck my calculations)
\n" ); document.write( " $\"n\"$ = the smaller odd integer
\n" ); document.write( " $\"n%2B2\"$ = the next (larger) odd integer
\n" ); document.write( "
\n" ); document.write( "What the problem says in words translates as
\n" ); document.write( " $\"%283%2F4%29%28n%2B2%29=%281%2F4%29n%2B5\"$ or $\"3%28n%2B2%29%2F4=n%2F4%2B5\"$
\n" ); document.write( "Multiplying times 4 to eliminate denominators, we get
\n" ); document.write( " $\"3%28n%2B2%29=n%2B5%2A4\"$
\n" ); document.write( " $\"3n%2B6=n%2B20\"$
\n" ); document.write( " $\"3n%2B6-n=20\"$
\n" ); document.write( " $\"3n-n=20-6\"$
\n" ); document.write( " $\"2n=14\"$
\n" ); document.write( " $\"n=14%2F2\"$
\n" ); document.write( " $\"highlight%28n=7%29\"$ --> $\"n%2B2=7%2B2\"$ --> $\"highlight%28n%2B2=9%29\"$
\n" ); document.write( "My solution has odd numbers, so it is a valid solution. \n" ); document.write( "

\n" );