Expert: Scott A Wilson - 1/13/2010

Question
I need help finding the five step method to solve the problem(s).

The question is:

One-half of a number is 25 more than one-third of the same number. What is the number?

And

The sum of a number and its reciprocal is 10/3(10 over 3). What is the number?

I don't need the answer i need to know the five-step method for solving them.

Thank you.

Answer
The number is N.

One half of the number is N/2.
One third of the number is N/3.
The question says that N/2 = 25 + N/3.

Multiplying by 2 and 3 is the same as multiplying by 6.
So lets multiply the entire equation by 6.

This gives 6*N/2 = 6*25 + 6*N/3.
That turns into 3N = 150 + 2N.

Subtracting 2N from both sides gives the answer.



The number is X.
The reciprocal is 1/X.
The question states that X + 1/X = 10/3.
Multiplying the entire equation by 3X gives 3X² + 3 = 10X.
Subtracting 10X from both sides gives 3X² - 10X + 3 = 0.
This factors into (3X + 1)(X + 3), so we have (3X + 1)(X + 3) = 0.
To solve, we wold have 3X+1=0 or x+3=0.  Solve both for the answer.