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)![]() ![]() You can put this solution on YOUR website! 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( " \n" ); document.write( "So, \n" ); document.write( "Since the product of their ages is 70, \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "Applying the quadratic formula to that last equation, \n" ); document.write( " \n" ); document.write( "The positive solution is \n" ); document.write( "The negative solution, \n" ); document.write( "does not make sense as Helen's age. \n" ); document.write( "So, Helen is |