document.write( "Question 1065231: Sally is 3 years older than Helen. The product of their ages is 70. How old is Sally? \n" ); document.write( "
Algebra.Com's Answer #680362 by KMST(5328)\"\" \"About 
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THE TIP:
\n" ); document.write( "To find pairs of whole-number factors of a number,
\n" ); document.write( "you can look to the prime factorization,
\n" ); document.write( "such as 70=2×5×7
\n" ); document.write( "and work from there.
\n" ); document.write( "
\n" ); document.write( "However, sometimes, it is easier to try possible factors,
\n" ); document.write( "starting with 1 and going up.
\n" ); document.write( "For example,
\n" ); document.write( "70=1×70
\n" ); document.write( "1 is always a factor,
\n" ); document.write( "but 2 also divides 70 evenly,
\n" ); document.write( "so we find that
\n" ); document.write( "70=2×35 .
\n" ); document.write( "We realize that 3, and 4 are not factors of 70,
\n" ); document.write( "but 5 is, and we find that
\n" ); document.write( "70=5×14 .
\n" ); document.write( "We know that 6=2×3 is not a factor of 70,
\n" ); document.write( "because we had figured out before that 3 is not a factor.
\n" ); document.write( "Next comes 7, and we know that
\n" ); document.write( "70=7×10.
\n" ); document.write( "The 4 pairs of factors listed above are all there is.
\n" ); document.write( "I know that because, for a pair of factors,
\n" ); document.write( "either both factors are the same,
\n" ); document.write( "as in 8×8=64 and 9×9=81,
\n" ); document.write( "or one factor is smaller,
\n" ); document.write( "and the other is larger.
\n" ); document.write( "Since 70 is between 64 and 81,
\n" ); document.write( "its pairs of factors will have
\n" ); document.write( "one factor smaller than 9,
\n" ); document.write( "and another one larger.
\n" ); document.write( "Since 4 is not a factor,
\n" ); document.write( "8=2×4 I
\n" ); document.write( "cannot be the smaller of a pair of factors,
\n" ); document.write( "so I stop looking for factor pairs after
\n" ); document.write( "7×10=70.
\n" ); document.write( "
\n" ); document.write( "THE ALTERNATE SOLUTION:
\n" ); document.write( "It is possible that your teacher expected you to set up and solve a quadratic equation. One way to do that:
\n" ); document.write( "\"x\"= Helen's age (defining a variable)
\n" ); document.write( "So, \"x%2B3\"= Sally's age.
\n" ); document.write( "Since the product of their ages is 70,
\n" ); document.write( "\"x%2A%28x%2B3%29=70\" is our equation.
\n" ); document.write( "\"x%28x%2B3%29=u0\" <---> \"x%5E2%2B3x=70\" <---> \"x%5E2%2B3x-70=0\"
\n" ); document.write( "Applying the quadratic formula to that last equation,
\n" ); document.write( "
\n" ); document.write( "The positive solution is \"x=%28-3%2B17%29%2F2=14%2F2=7\"
\n" ); document.write( "The negative solution, \"x=%28-3-17%29%2F2=%28-20%29%2F2=-10\" ,
\n" ); document.write( "does not make sense as Helen's age.
\n" ); document.write( "So, Helen is \"x=7\" , and Sally is \"x%2B3=7%2B3=highlight%2810%29\" .
\n" ); document.write( "
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