document.write( "Question 603906: The number n is a two digit number. When n is divided by 10 the remainder is 9, when n is divided by 9 the remainder is 8. What is the value of n? \n" ); document.write( "

Algebra.Com's Answer #380958 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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The number n is a two digit number.
\n" ); document.write( " When n is divided by 10 the remainder is 9, when n is divided by 9 the remainder is 8.
\n" ); document.write( " What is the value of n?
\n" ); document.write( ":
\n" ); document.write( " $\"n%2F10\"$ has remainder of 9, Second digit has to be 9
\n" ); document.write( "19, 29, 39, 49, 59, 69, 79, 89, 99
\n" ); document.write( ":
\n" ); document.write( " $\"n%2F9\"$ has remainder of 8
\n" ); document.write( "26, 35, 44, 53, 62, 71, 80, 89, 98
\n" ); document.write( ":
\n" ); document.write( "n = 89 \r
\n" ); document.write( "\n" ); document.write( "This is the brute force method, here is a formula, not quite sure why it works
\n" ); document.write( " $\"%28n-8%29%2F9\"$ = $\"n-9%29%2F10\"$ = 1
\n" ); document.write( "multiply by 90 to clear the denominators
\n" ); document.write( "10(n-8) - 9(n-9) = 1
\n" ); document.write( "10n - 80 - 9n + 81 = 90
\n" ); document.write( "n + 1 = 90
\n" ); document.write( "n = 90- 1
\n" ); document.write( "n = 89 \n" ); document.write( "

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