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You can put this solution on YOUR website!
let s represent sue's age now.
\n" ); document.write( "let c represent candice's age now.
\n" ); document.write( "your answer is:
\n" ); document.write( "s equals 4 and c equals 9.
\n" ); document.write( "2 years from now s will be equal to 6 and c will be equal to 11.
\n" ); document.write( "1 year ago s was equal to 3 and c was equal to 8.
\n" ); document.write( "the problems states that the product of their ages 2 years from now will be 18 more than twice the product of their ages a year ago.
\n" ); document.write( "using the solutions found, this equation becomes:
\n" ); document.write( "6 * 11 = 18 + 2 * 3 * 8 which simplifies to:
\n" ); document.write( "66 = 18 + 48
\n" ); document.write( "simplify this to get:
\n" ); document.write( "66 = 66 which confirms the numbers are good.
\n" ); document.write( "how did we get it?
\n" ); document.write( "today sue is 5 years younger than candice.
\n" ); document.write( "this translates to:
\n" ); document.write( "s = c - 5
\n" ); document.write( "2 years from now the product of sue's age and candice's age will be:
\n" ); document.write( "(s + 2) * (c - 5 + 2) which becomes:
\n" ); document.write( "(s + 2) * (c - 3)
\n" ); document.write( "1 year ago, the product of sue's age and candice's age was:
\n" ); document.write( "(s - 1) * (c - 5 - 1) which became:
\n" ); document.write( "(s - 1) * (c - 6)
\n" ); document.write( "the equations we will be working with are:
\n" ); document.write( "(s + 2) * (c - 3) which is the product of their ages 2 years from now.
\n" ); document.write( "(s - 1) * (c - 6) which is the product of their ages 1 year ago.
\n" ); document.write( "the formula we will be using is:
\n" ); document.write( "product of their ages 2 years from now is equal to 18 plus [ 2 times the product of their ages 1 year aqo ].
\n" ); document.write( "this becomes:
\n" ); document.write( "(s+2) * (c-3) = 18 + [ 2 * (s-1) * (c-6) ]
\n" ); document.write( "you need to multiply these out to get:
\n" ); document.write( "sc - 3s + 2c - 6 = 18 + 2 * (sc - 6s - c + 6)
\n" ); document.write( "simplify this to get:
\n" ); document.write( "sc - 3s + 2c - 6 = 18 + 2sc - 12s - 2c + 12
\n" ); document.write( "add 12s and 2c to both sides of this equation to get:
\n" ); document.write( "sc - 3s + 12s + 2c + 2c - 6 = 18 + 2sc + 12
\n" ); document.write( "simplify this by combining like terms to get:
\n" ); document.write( "sc + 9s + 4c - 6 = 30 + 2sc
\n" ); document.write( "subtract 2sc from both sides of this equation to get:
\n" ); document.write( "-sc + 9s + 4c - 6 = 30
\n" ); document.write( "add 6 to both sides of this equation to get:
\n" ); document.write( "-sc + 9s + 4c = 36
\n" ); document.write( "since s = c - 5, substitute for s in this equation to get:
\n" ); document.write( "-((c-5)*c) + 9*(c-5) + 4c = 36
\n" ); document.write( "simplify to get:
\n" ); document.write( "-c^2 + 5c + 9c - 45 + 4c = 36
\n" ); document.write( "combine like terms to get:
\n" ); document.write( "-c^2 + 18c - 45 = 36
\n" ); document.write( "add 45 to both sides of this equation to get:
\n" ); document.write( "-c^2 + 18c = 81
\n" ); document.write( "add c^2 and subtract 18c from both sides of this equation to get:
\n" ); document.write( "0 = c^2 - 18c + 81 which is the same as:
\n" ); document.write( "c^2 - 18c + 81 = 0
\n" ); document.write( "factor this quadratic equation to get:
\n" ); document.write( "(c-9) * (c-9) = 0
\n" ); document.write( "this results in c = 9.
\n" ); document.write( "since s = c - 5, this results in s = 4
\n" ); document.write( "your answer is s = 4 and c = 9 as shown and confirmed way up top at the beginning of this exercise.\r
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