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
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. 4 Answer by ptaylor(2198) (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
