document.write( "Question 702435: Four years from now a mother will be 5 times the age of her daughter. At present she will be 9 times the age of her daughter. (Please use substitution or elimination and show steps.) \n" ); document.write( "
Algebra.Com's Answer #433021 by math-vortex(648) $\"\"$ $\"About$
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document.write( "Hi, there--\r\n" );
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document.write( "The Problem\r\n" );
document.write( "Four years from now a mother will be 5 times the age of her daughter. At present she will be 9 times \r\n" );
document.write( "the age of her daughter.\r\n" );
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document.write( "A Solution\r\n" );
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document.write( "First, we choose our variables:\r\n" );
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document.write( "Let m be the current age of the mother.\r\n" );
document.write( "Let d be the current age  of the daughter.\r\n" );
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document.write( "The age of the mother five years from now is m+4.\r\n" );
document.write( "The age of the daughter five years from now is d+4.\r\n" );
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document.write( "Now, we write two equations using our variables that describe the relationships between the age of \r\n" );
document.write( "the mother and the age of the daughter. \r\n" );
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document.write( "The first half of the problem states, \"Four years from now a mother will be 5 times the age of her \r\n" );
document.write( "daughter.\" In algebra, we can write this relationship as,\r\n" );
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document.write( "The second part of the problem states, \"At present she will be 9 times the age of her daughter.\"\r\n" );
document.write( "In algebra, we can write,\r\n" );
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document.write( "We now have a system of two equations with two variables. We will solve this using the substitution \r\n" );
document.write( "method. (The elimination method would also work, of course.)\r\n" );
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document.write( "Substitute 9d for m in the first equation.\r\n" );
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document.write( "We solve for d. Clear the parentheses using the distributive property.\r\n" );
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document.write( "Isolate the variable d by subtracting 5d from both sides of the equation.\r\n" );
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document.write( "Combine like terms. 9d-5d=4d on the left side and 5d-5d=0 on the right side.\r\n" );
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document.write( "Subtract 5 from both sides.\r\n" );
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document.write( "Simplify.\r\n" );
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document.write( "Divide both sides of the equation by 4 in order to find the value of d.\r\n" );
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document.write( "In the context of this problem, the equation d=4 means that the daughter is currently 4 years old. To \r\n" );
document.write( "find the mother's current age, substitute 4 for d in either of the original equations. (I'll use the second.)\r\n" );
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document.write( "The mother is currently 36 years old.\r\n" );
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document.write( "Our last step is to heck our answers in both equations. Often, if you make an error. Your answer will \r\n" );
document.write( "work in one equation but not the other. ALWAYS check both equations! (o:\r\n" );
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document.write( "Substitute 4 for d and 36 for m in each equation.\r\n" );
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document.write( "Good! The two sides of the equation are equal.\r\n" );
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document.write( "Good!\r\n" );
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document.write( "You can also check by using the ages you found in the written problem statement:\r\n" );
document.write( "\"Four years from now a mother will be 5 times the age of her daughter.\"\r\n" );
document.write( "Four years from now, the mother will be 36+4=40 years old. The Daughter will be 4+4=8 years old. \r\n" );
document.write( "Since 40 is five times eight, our numbers work for the first part of the problem.\r\n" );
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document.write( "\"At present she will be 9 times the age of her daughter.\"\r\n" );
document.write( "At present the mother is thirty-six years old, and the daughter is nine years old. Thirty-six is nine \r\n" );
document.write( "times four, so part two is also satisfied.\r\n" );
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document.write( "That's it. You may email me at math.in.the.vortex@gmail.com  if you have questions about the solution. \r\n" );
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document.write( "Mrs.Figgy\r\n" );
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