SOLUTION: I need to use the following 5-step method to solve this problem. 1. State what you need to solve for. 2. Identify the unknowns. 3. Write the equation derived from the word probl

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Question 413910: I need to use the following 5-step method to solve this problem.
1. State what you need to solve for.
2. Identify the unknowns.
3. Write the equation derived from the word problem.
4. Solve for the given variable.
5. Check.
Here is the question.
>>>>>>The sum of a number and its reciprocal is (10/3). What is the number?
This is what I think the answer should be. Am I thinking this out correctly?
1. I need to solve for a number.
2. The unknown is x.
3. The formula is x + (1/x) = (10/3)
4. Solve. I thought to do
3(x + (1/x)) = (10/3)3
3x+ 3/x = 10
( I think I am stuck. I don't think I have the right formula. What do I do?
Thanks alot for your help.
:)
Answer by bayners123(12) (Show Source):
You can put this solution on YOUR website!
Yeah you are well on your way, just multiply through by x and solve the quadratic.
you should get
Rearranging gives
so factorise to (3x-1)(x-3)=0, and from this we can see x is 3 or 1/3, both of which fit the description.
As for the wordy stuff, I am not too familiar with that but it seemed to make sense.