document.write( "Question 872376: Amother is three times as old as her child seven years ago the products of their ages was 104 find the present age of the child? \n" ); document.write( "
Algebra.Com's Answer #526123 by josmiceli(19441)\"\" \"About 
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Let \"+m+\" = the mother's age now
\n" ); document.write( "Let \"+p+\" = the child's age now
\n" ); document.write( "------------------------------
\n" ); document.write( "(1) \"+m+=+3p+\"
\n" ); document.write( "(2) \"+%28+m+-+7+%29%2A%28+p+-+7+%29+=+104+\"
\n" ); document.write( "-----------------------------
\n" ); document.write( "(2) \"+m%2Ap+-+7p+-+7m+%2B+49+=+104+\"
\n" ); document.write( "(2) \"+m%2Ap+-+7%2A%28+p+%2B+m+%29+=+104+-+49+\"
\n" ); document.write( "(2) \"+m%2Ap+-+7%2A%28+p+%2B+m+%29+=+55+\"
\n" ); document.write( "Substitute (1) into (2)
\n" ); document.write( "(2) \"+3p%2Ap+-+7%2A%28+p+%2B+3p+%29+=+55+\"
\n" ); document.write( "(2) \"+3p%5E2+-+28p+-+55+=+0+\"
\n" ); document.write( "---------------------------
\n" ); document.write( "Solve using the quadratic formula
\n" ); document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"
\n" ); document.write( "\"+a+=+3+\"
\n" ); document.write( "\"+b+=+-28+\"
\n" ); document.write( "\"+c+=+-55+\"
\n" ); document.write( "\"+p+=+%28-%28-28%29+%2B-+sqrt%28+%28-28%29%5E2-4%2A3%2A%28-55%29+%29%29%2F%282%2A3%29+\"
\n" ); document.write( "\"+p+=+%28+28+%2B-+sqrt%28+784+%2B+660+%29%29%2F6+\"
\n" ); document.write( "\"+p+=+%28+28+%2B-+sqrt%28+1444+%29%29%2F6+\"
\n" ); document.write( "\"+p+=+%28+28+%2B+38%29%2F6+\" ( can't use the negative square root )
\n" ); document.write( "\"+p+=++66%2F6+\"
\n" ); document.write( "\"+p+=+11+\"
\n" ); document.write( "--------------
\n" ); document.write( "(1) \"+m+=+3p+\"
\n" ); document.write( "(1) \"+m+=+3%2A11+\"
\n" ); document.write( "(1) \"+m+=+33+\"
\n" ); document.write( "The mother is 33 and the child is 11
\n" ); document.write( "check:
\n" ); document.write( "(2) \"+%28+m+-+7+%29%2A%28+p+-+7+%29+=+104+\"
\n" ); document.write( "(2) \"+%28+33+-+7+%29%2A%28+11+-+7+%29+=+104+\"
\n" ); document.write( "(2) \"+26%2A4+=+104+\"
\n" ); document.write( "(2) \"+104+=+104+\"
\n" ); document.write( "OK
\n" ); document.write( "
\n" );