The product of 5 and the sum of two and a number is five times the number. find the number.

Question

I want to know how to write the problem out. 

Answer 1

The key to solving word (story) problems is to correctly translate the words and phrases into precise, concise math expressions (with variables and operations).
 
Make a table of these translations as you use them:
    "is"  means  =
    " five times the number"   means   5x     (if x is the number)
    "product"    means the result of multiplication
    "sum"       means the result of addition
 
So.
 
Let x = the number
We are to find x.
 
"The product of 5 and the sum of two and a number is five times the number"   means
                              5    *   (              2           +          x     )      =     5    *       x
 
Now, the math is easy (but watch for math difficulties).
 

Answer 2

Let x be the unknown number:

• The product of 5 and the sum of two and the number: 5*(2+x)
• is five times the number = 5x

 

5(2+x) = 5x

 

Divide both sides by 5:

 

2 + x = x

 

Subtract x from both sides:

 

2 = 0

 

When you get a nonsense result like 2=0, it means that there is no solution to the equation; that is, there is no number that equals itself plus 2 (2+x=x).