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

Hope this helps---ptaylor
RELATED QUESTIONS
If a certain number is added to 5 times the reciprocal of two more than that number, the... (answered by MathTherapy)

One positive number is 10 less than another positive number. If the reciprocal of the... (answered by ankor@dixie-net.com)

What is the equation for: if a certain positive number is added to 8 times the reciprocal (answered by lwsshak3)

If 1/6 is added to 4 times the reciprocal of a certain number, the result is 21/10. Find... (answered by Theo)

Where 3 times a certain number is added to twice its reciprocal the result is 5. What is... (answered by ptaylor)

If the reciprocal of a certain number x is added to 5/3 the result is 2. what is... (answered by edjones)

if 10 be added to 4 times a certain number , the result is 5 less than five times the... (answered by ankor@dixie-net.com)

If 20 is added to the 8 times of a certain number the result is 10 less than ten times... (answered by Fombitz)

if the reciprocal of a certain positive number is one less than twice that number, find... (answered by MRperkins)