document.write( "Question 825721: In two years, Mr. Victoria will be thrice the age of his son, Bing. Six yeas ago, he was five times Bing's age. How old is each at present? \n" ); document.write( "
Algebra.Com's Answer #497643 by math-vortex(648)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Hi, there--\r\n" );
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document.write( "THE PROBLEM:\r\n" );
document.write( "In two years, Mr. Victoria will be thrice the age of his son, Bing. Six yeas ago, he was five times \r\n" );
document.write( "Bing's age. How old is each at present?\r\n" );
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document.write( "A SOLUTION:\r\n" );
document.write( "This is a solution using two variables. One can also solve this using only one variable. (Please \r\n" );
document.write( "email be if you would like to see the one-variable solution.)\r\n" );
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document.write( "Let v be the age of Mr. Victoria at present.\r\n" );
document.write( "Let b be the age of Bing at present.\r\n" );
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document.write( "Write two equations modeling the relationships is the problem.\r\n" );
document.write( "FIRST EQUATION: \"In two years, Mr. Victoria will be thrice the age of his son, Bing.\"\r\n" );
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document.write( "In two years, Mr Victoria will be 2 years older so his age will be v+2.\r\n" );
document.write( "In two years, Bing's age will be b+2.\r\n" );
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document.write( "Mr. Victoria will be thrice (three times) the age of Bing, so our equation is\r\n" );
document.write( "v + 2 = 3*(b + 2)\r\n" );
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document.write( "SECOND EQUATION: \"Six yeas ago, he was five times Bing's age.\"\r\n" );
document.write( "Six years ago, Mr. Victoria was 6 years younger; his age was v-6.\r\n" );
document.write( "Likewise, Bing 's age was b-6.\r\n" );
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document.write( "Mr. Victoria was 5 times Bing's age, so our equation is\r\n" );
document.write( "v-6 = 5*(b - 6)\r\n" );
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document.write( "We now have a system of two equations in two variables. We can solve for v and b using the \r\n" );
document.write( "substitution method.\r\n" );
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document.write( "Simplify the first equation and rewrite in\"v=\" form.\r\n" );
document.write( "v + 2 = 3*(b + 2)\r\n" );
document.write( "v + 2 = 3b + 6\r\n" );
document.write( "v = 3b + 6 - 2\r\n" );
document.write( "v = 3b + 4\r\n" );
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document.write( "Substitute 3b + 4 for v in the second equation.\r\n" );
document.write( "v - 6 = 5*(b - 6)\r\n" );
document.write( "(3b + 4) - 6 = 5*(b - 6)\r\n" );
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document.write( "Simplify and solve for b.\r\n" );
document.write( "3b + 4 - 6 = 5b - 30\r\n" );
document.write( "3b - 2 = 5b - 30\r\n" );
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document.write( "Subtract 5b from both sides of the equation. (3b-5b=-2b and 5b-5b=0)\r\n" );
document.write( "-2b - 2 = -30\r\n" );
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document.write( "Add 2 to both sides of the equation. (-2+2=0)\r\n" );
document.write( "-2b = -28\r\n" );
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document.write( "Divide both sides of the equation by -2. (-2b/-2=b and -28/-2=14)\r\n" );
document.write( "b = 14\r\n" );
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document.write( "In the context of this problem, b=14 means that Bing is 14 years old at present. We can use \r\n" );
document.write( "either equation to determine Mr. Victoria's age. I'll use the first equation we simplified.\r\n" );
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document.write( "v = 3b + 4\r\n" );
document.write( "v = 3(14) + 4\r\n" );
document.write( "v = 42 + 4\r\n" );
document.write( "v = 46\r\n" );
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document.write( "The equation v=46 means that Mr. Victoria is 46 years old at present.\r\n" );
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document.write( "It's a good idea to check your numbers with the wording of the original problem.\r\n" );
document.write( "\"In two years, Mr. Victoria will be thrice the age of his son, Bing.\"\r\n" );
document.write( "In two years, Mr. Victoria will be 48 and Bing will be 16. We know that 46 is thrice 16. CHECK!\r\n" );
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document.write( "\"Six yeas ago, he was five times Bing's age.\"\r\n" );
document.write( "Six years ago Mr. Victoria was 40 and Bing was 8. We know that 40 is 5 times 8. CHECK!\r\n" );
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document.write( "Hope this helps! Feel free to email me if you has questions about this (or want the \r\n" );
document.write( "one-variable solution.)\r\n" );
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document.write( "Mrs. Figgy\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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