document.write( "Question 1204109: my number is 25.3 divided by a number with 1 decimal digit it gives me a quotient greater than 10 but less than 11 what is my number? \n" ); document.write( "

Algebra.Com's Answer #840151 by math_tutor2020(3817) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "x = the number you are dividing over
\n" ); document.write( "It must be a positive number so that $\"%2825.3%29%2F%28x%29\"$ is between the two positive numbers 10 and 11.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"10+%3C+%2825.3%29%2F%28x%29+%3C+11\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"10x+%3C+x%2A%28%2825.3%29%2F%28x%29%29+%3C+11x\"$ Multiply all three sides by x. Multiplying all sides by a positive number does not flip the inequality signs.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"10x+%3C+25.3+%3C+11x\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "That last inequality breaks down into these two inequalities
\n" ); document.write( " $\"10x+%3C+25.3+\"$ and $\"25.3+%3C+11x+\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Solve $\"10x+%3C+25.3+\"$ to get $\"+x+%3C+2.53\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Solve $\"25.3+%3C+11x+\"$ to get $\"x+%3E+2.3\"$ aka $\"+2.3+%3C+x\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "We found that $\"+2.3+%3C+x\"$ and $\"+x+%3C+2.53\"$ .
\n" ); document.write( "Glue those together to get $\"2.3+%3C+x+%3C+2.53\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Here's a table of examples
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "

x	(25.3)/x	Result greater than 10 but less than 11?
2.28	11.0965	no
2.3	11	no
2.32	10.9052	yes
2.34	10.812	yes
2.36	10.7203	yes
2.38	10.6303	yes
2.4	10.5417	yes
2.42	10.4545	yes
2.44	10.3689	yes
2.46	10.2846	yes
2.48	10.2016	yes
2.5	10.12	yes
2.52	10.0397	yes
2.54	9.9606	no

\n" ); document.write( "With the exception of the results 11 and 10.12, each of the values in the 2nd column are approximate.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "If we rounded to one decimal place, then the only possible x solutions would be: x = 2.4 and x = 2.5\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "x = 2.3 doesn't work since $\"10+%3C+%2825.3%29%2F%28x%29+%3C+11\"$ becomes $\"10+%3C+%2825.3%29%2F%282.3%29+%3C+11\"$ and then simplifies to $\"10+%3C+11+%3C+11\"$ which is false.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "But x = 2.4 does work
\n" ); document.write( " $\"10+%3C+%2825.3%29%2F%28x%29+%3C+11\"$ becomes $\"10+%3C+%2825.3%29%2F%282.4%29+%3C+11\"$ and then simplifies to $\"10+%3C+10.54+%3C+11\"$ which is true\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "x = 2.5 also works as well
\n" ); document.write( " $\"10+%3C+%2825.3%29%2F%28x%29+%3C+11\"$ becomes $\"10+%3C+%2825.3%29%2F%282.5%29+%3C+11\"$ and then simplifies to $\"10+%3C+10.12+%3C+11\"$ which is true.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Answer: The mystery number is either 2.4 or 2.5
\n" ); document.write( " \n" ); document.write( "

\n" );