# SOLUTION: Mary is twice as old as Rachel will be in seven years. Four years ago, Mary was four times as old as Rachel. How old is Mary now?

Algebra ->  Algebra  -> Coordinate Systems and Linear Equations -> SOLUTION: Mary is twice as old as Rachel will be in seven years. Four years ago, Mary was four times as old as Rachel. How old is Mary now?      Log On

 Ad: You enter your algebra equation or inequality - Algebrator solves it step-by-step while providing clear explanations. Free on-line demo . Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help! Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

 Linear Solvers Practice Answers archive Word Problems Lessons In depth

 Question 126838: Mary is twice as old as Rachel will be in seven years. Four years ago, Mary was four times as old as Rachel. How old is Mary now?Answer by ankor@dixie-net.com(15747)   (Show Source): You can put this solution on YOUR website!Let M = Mary's age now Let R = Rachel's age now : Write an equation for each statement: : Mary is twice as old as Rachel will be in seven years. M = 2(R+7) : Four years ago they would be: (M-4) (R-4) : Four years ago, Mary was four times as old as Rachel. (M-4) = 4(R-4); just do some basic algebra here M - 4 = 4R - 16 M = 4R - 16 + 4 M = 4R - 12 Substitute 2(R+7) for M, find R 2(R+7) = 4R - 12 2R + 14 = 4R - 12 2R - 4R = -12 - 14 -2R = -26 R = R = + 13 yrs is Rachel's age now : How old is Mary now? : We know that M = 2(R+7); substitute 13 for R M = 2(13+7) M = 2(20) M = 40 yrs is Mary's age now : : Check solutions in the statement: "Four years ago, Mary was four times as old as Rachel." (40-4) = 4(13 - 4) 36 = 4(9); confirms our solution ; ; Did this make sense to you? This is a good method to do all these kind of problems; First thing, write an equation for each statement. Let the basic operations of algebra carry you thru. Let me know what you think.