brb... five what?
The key is in the word "a number". We do not know what this number is and we want to find out what it is since we were told in the second sentence: Find the number!
It is always a good idea to name (by a single letter) any number you do not know but you want to find out what it is. You can even choose the letter to name this number. But since I am writing this without you being around I will have to choose the letter for you. I choose g! (Normally people choose x but I am different). Once you are happy with naming the number then you will need to translate the problem statement using the name of the number instead of "a number" or "the number". At the same time we can translate English words for various operators with the symbols we learned in Algebra. So, here it goes:
Original Statement:
five divided by the difference of a number and 12 equals the quotiene of 10 and the sum of the number and five. Find the number
Translation:
5 /(g - 12) = 10 /(g + 5). Find g
Quite a translation! Much shorter than the original. Good thing is that we can now work on this using the principles of solving equations, which is what the first sentence translate into.
Solution process:5 /(g - 12) = 10 /(g + 5) .... balance (multiply both sides of the equation by (g-12)(g+5))
5(g + 5) = 10(g - 12) .... simplify (expand the brackets)
5g + 25 = 10g - 120 .... balance (add 120 - 5g to both sides of the equation)
145 = 5g .... balance (divide by 5 both sides of the equation)
29 = g .... done!The answer is: the number is 29! We can check:
5 /(29 - 12) = 5/17 = 10/34 = 10 /(29 + 5)