SOLUTION: one third of a number is 5 less than half of the same number. What is the number? Once you figure the answer how would you show your work to check to make sure it is right?

Question 86522This question is from textbook algebra structure and method
: one third of a number is 5 less than half of the same number. What is the number?
Once you figure the answer how would you show your work to check to make sure it is right? This question is from textbook algebra structure and method

Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Probably the hardest part of doing this kind of problem is translating from the English statement into algebra.
One third of a number (n/3) is (=) five less than half the number ((n/2)-5). So you can write:
n/3 = (n/2)-5 Multiply through by 6 (the LCD) to clear the fractions.
6(n/3 = (n/2)-5)
2n = 3n-30 Add 30 to both sides.
2n+30 = 3n Finally, subtract 2n from both sides.
30 = n or n = 30
The number is 30.
To check the answer. substitute 30 for n in the initial equation.
30/3 = (30/2)-5 Evaluate this.
10 = 15-5
10 = 10
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