SOLUTION: One third of a number is 5 less than half of the number. What is the number? I need to set this up using the five step method to solve and check. Iam helping my nephew with s

Question 174564: One third of a number is 5 less than half of the number. What is the number?
I need to set this up using the five step method to solve and check. Iam helping my nephew with some homework over break, so i need to sit down with him and explain the steps, thanks
Found 2 solutions by rapaljer, Mathtut:
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
I'm not sure whose 5 step method you need to use. I have my own 5 step method.

Step 1: Identify the variable.
Let x = the number

Step 2: Write the equation.

Step 3: Solve the equation.
In this case, multiply both sides times the LCD for the equation which is 6.

Step 4: Answer the question. The number is 30.

Step 5: Check. Substitute 30 for the number and see if it works.
One third of 30 (which would be 10) is 5 less than half the number (which would be 15. 10 is indeed 5 less than 15, so it checks.

For additional explanation on Word Problems, please see my own website. You can click on my tutor name "rapaljer" anywhere in algebra.com. Take the first main link on my homepage, which is "Basic, Intermediate, and College Algebra: One Step at a Time." Then select "Basic Algebra", look for Chapter 1, and you will find a couple of sections on Word Problems. In this Chapter, you will find complete explanations, examples, exercises, and answers in a user-friendly format, all completely FREE. In addition, I have solved a LOT of the problems from this in my MATH IN LIVING COLOR pages. In fact, for anyone who can't remember my name, you can also find my website by doing a Google search for "Math in Living Color". My homepage should be at the top of such a search. Good luck to your nephew! Encourage him to do LOTS of homework! It's the only way to really get good at math!!

R^2
Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
not quite sure what those 5 steps are so since you have access to what the book says about the 5 steps hopefully you can work those five steps from this solution:
:
lets call call the unknown number x
:
one third of x = 5 less (subtraction from) 1/2 of x
:
1/3(x)=1/2(x)-5
:
multiply all terms by Least common multiple of 6
:
2x=3x-30....subtract 3x from both sides
:
-x=-30.....divide by -1 on both sides
:

:
checking:
1/3(30)=1/2(30)-5
:
10=15-5
:
10=10......checked

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