document.write( "Question 208027: in 3 years,alex will be 3 times as old as his sister precy,a year ago alex was 7 times as old as precy.how old are they now
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Algebra.Com's Answer #157365 by Theo(13342)![]() ![]() You can put this solution on YOUR website! in 3 years, alex will be 3 times as old as his sister precy, a year ago alex was 7 times as old as precy. how old are they now \n" ); document.write( "----- \n" ); document.write( "alex is x years old now \n" ); document.write( "precy is y years old now \n" ); document.write( "----- \n" ); document.write( "in 3 years, alex will be 3 times as old as his sister precy \n" ); document.write( "3 years from now, alex will be (x + 3) years old. \n" ); document.write( "3 years from now, precy will be (y + 3) years old. \n" ); document.write( "3 years from now, alex will be 3 times as old as his sister precy. \n" ); document.write( "equation for this would be: \n" ); document.write( "(x + 3) = 3 * (y + 3) \n" ); document.write( "----- \n" ); document.write( "a year ago alex was 7 times as old as precy. \n" ); document.write( "a year ago, alex was (x-1) years old. \n" ); document.write( "precy was (y-1) years old. \n" ); document.write( "a year ago, alex was 7 times as old as precy. \n" ); document.write( "equation for this would be: \n" ); document.write( "(x - 1) = 7 * (y - 1) \n" ); document.write( "----- \n" ); document.write( "you have 2 equations that express the relationship between alex's age and precy's age. \n" ); document.write( "those 2 equations are: \n" ); document.write( "(x + 3) = 3 * (y + 3) \n" ); document.write( "and \n" ); document.write( "(x - 1) = 7 * (y - 1) \n" ); document.write( "----- \n" ); document.write( "you need to solve both equations simultaneously to get the same solution that satisfies both equations at the same time. \n" ); document.write( "----- \n" ); document.write( "simplifying these equations and converting them to standard form, they become: \n" ); document.write( "x - 3y = 6 \n" ); document.write( "and \n" ); document.write( "x - 7y = -6 \n" ); document.write( "----- \n" ); document.write( "if we subtract the second equation from the first, then the x will cancel out and we'll get: \n" ); document.write( "4y = 12 \n" ); document.write( "divided both sides of the equation by 4 gets: \n" ); document.write( "y = 3 \n" ); document.write( "if y = 3, we can then solve for x in either equation: \n" ); document.write( "from the first equation, we get: \n" ); document.write( "x - 9 = 6 resulting in x = 15 \n" ); document.write( "from the second equation, we get: \n" ); document.write( "x - 7y = -6 which becomes x - 21 = -6 \n" ); document.write( "this results in x = 15 \n" ); document.write( "----- \n" ); document.write( "alex is 15 years old now. \n" ); document.write( "precy is 3 years old now. \n" ); document.write( "----- \n" ); document.write( "1 year ago alex was 14 years old and precy was 2 years old. \n" ); document.write( "14 / 2 = 7 satisfying the part of the equation for one year ago. \n" ); document.write( "----- \n" ); document.write( "3 years from now alex will be 18 years old and precy will be 6 years old. \n" ); document.write( "18 / 6 = 3 satisfying the part of the equation for 3 years from now. \n" ); document.write( "----- \n" ); document.write( "answer to the question is alex is 15 years old and precy is 3. \n" ); document.write( "----- \n" ); document.write( " |