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Five times a number is divided by 7 more than that number. If the result is 0 then what was the original number?

 Apr 29, 2023
 #1
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Five times a number is divided by 7 more than that number. If the result is 0 then what was the original number?

 

          5n  

       –––––  =  0  

        n + 7  

 

The only way this can happen is n = zero.   

.  

 Apr 29, 2023
 #2
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When five times a number is divided by 7 more than the number and the result is 2, then the number is 14/3, which is solved using the linear equation in one variable 5x/(x+ 7) = 2, where x is the required number.

What are linear equations in one variable?

Linear equations are first-order equations. Lines in the coordinate system are determined by linear equations. A linear equation in one variable is defined as an equation with a homogeneous variable of degree 1 (i.e. only one variable).

How to solve the given question?

In the question, we are asked to find a number, which satisfies the statement, "Five times a number is divided by 7 more than the number. The result of this division is 2".

We assume the number to be x.

Now we try to form a linear equation in one variable from the given statement.

Five times a number is 5x.

7 more than a number is x + 7.

We are said that five times a number is divided by 7 more than a number. This can be shown as 5x/(x + 7).

Now, the result is given as 2, which can be shown as:

5x/(x+ 7) = 2, which is the required linear equation in one variable.

To get the number, we solve the equation using the following steps:

5x/(x+ 7) = 2

or, {5x/(x+ 7)}*(x + 7) = 2*(x + 7) (Multiplying both sides by (x + 7))

or, 5x = 2x + 14 (Simplifying)

or, 5x - 2x = 2x + 14 - 2x (Subtracting 2x from both sides)

or, 3x = 14 (Simplifying)

or, 3x/3 = 14/3 (Dividing both sides by 3)

or, x = 14/3 (Simplifying)

∴ When five times a number is divided by 7 more than the number and the result is 2, then the number is 14/3, which is solved using the linear equation in one variable 5x/(x+ 7) = 2, where x is the required number.

 May 1, 2023

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