# SOLUTION: If a certain positive number is added to 4 times the reciprocal of 10 less than the number, the result is 5. What is one of the numbers? a. -6 b. -10 c. -9 d. 4

Algebra ->  Algebra  -> Coordinate Systems and Linear Equations  -> Lessons  -> Linear Equations Lesson -> SOLUTION: If a certain positive number is added to 4 times the reciprocal of 10 less than the number, the result is 5. What is one of the numbers? a. -6 b. -10 c. -9 d. 4      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: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

 Linear Solvers Practice Answers archive Word Problems Lessons In depth

 Question 132598: If a certain positive number is added to 4 times the reciprocal of 10 less than the number, the result is 5. What is one of the numbers? a. -6 b. -10 c. -9 d. 4Answer by ptaylor(2048)   (Show Source): You can put this solution on YOUR website!Let x=the certain positive number 10 less than this number is x-10 The reciprocal of 10 less than the number is 1/(x-10) 4 times the reciprocal is 4/(x-10) Now we are told the following: x + 4/(x-10)=5 multiply each term by (x-10) x(x-10)+4=5(x-10) get rid of parens x^2-10x+4=5x-50 subtract 5x from and add 50 to both sides x^2-10x-5x+4+50=5x-5x-50+50 collect like terms x^2-15x+54=0 quadratic in standard form and it can be factored: (x-6)(x-9)=0 x-6=0 x=6-----------------------possible solution x-9=0 x=9---------------------------another possible solution CK for x=6 6+4/(6-10)=5 6-1=5 5=5-----------------------------x=6 is a solution for x=9 6+4/(9-10)=5 6-4=5 2=5------------------------------x=9 is not a solution Hope this helps---ptaylor