document.write( "Question 1170802: Good day please may you assist me in the following question. \r
\n" ); document.write( "\n" ); document.write( "Consider the integers x and y. when y is divided by x the remainder is 29. when y is divided by x/2, the remainder is 13. determine x. \n" ); document.write( "

Algebra.Com's Answer #797487 by mahikab(11) $\"\"$ $\"About$

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Given that when y is divided by x the remainder is 29.
\n" ); document.write( "=> y = q*x + 29, where q is quotient [1]
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\n" ); document.write( "Also given that when y is divided by x/2, the remainder is 13.
\n" ); document.write( "=> y = p*x/2 + 13, where p is quotient [2]
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\n" ); document.write( "So we can write, qx + 29 = px/2 + 13
\n" ); document.write( "Multiple both sides by 2, 2qx + 58 = px + 26
\n" ); document.write( "or, px - 2qx = 58 - 26
\n" ); document.write( "x(p - 2q) = 32
\n" ); document.write( "x = 32/(p - 2q) and this is the value of x.
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\n" ); document.write( "You can choose selective values of p and q to get the integer value of x.
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\n" ); document.write( "For example, assuming q = 0 and p = 1, x = 32
\n" ); document.write( "So from [2] above: y = 1*32/2 + 13 = 16 + 13 = 29
\n" ); document.write( "Now if you divide 29 by 16 (x/2), the remainder is 13 while if you divide 29 by 32, the remainder is 29.
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\n" ); document.write( "So, the solution is: $\"x+=+32%2F%28p+-+2q%29\"$ , where q and p are quotients as assumed above. \n" ); document.write( "

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