if you add 2/5 of a number to the number itself, you get 56. what is the number?

Question

 if you add 2/5 of a number to the number itself, you get 56. what is the number?

Answer 1

Hi Christina--

 

Another way to do this is to take the original equation

 

2/5n + n = 56

 

and get ride of the fraction by multiplying everything by 5, so

 

2n + 5n = 280, which means that 7n = 280, so...

 

n = 40

 

2/5 of 40 = 2/5 * 40, which = 80/5, which = 16

 

40 + 16 = 56

 

Hope this helps!

 

Matt in NY

Answer 2

Hello Christina.  As I'm sure you know, this is an algebra problem at the core.  There is a number that satisfies the relationship described in the problem.  Let's call that number "x" (from "the number itself").  From the problem, we know that "x" has to be added to something and in this case, that something is equal to 2/5 of "x".  The sum of these two is equal to 56.  From here, we can write a number sentence including our unknown "x".

 

(2/5 * x) + x = 56

 

The sum on the left side of the equation can be simplified by recalling that any number times 1 is equal to itself.  We can rewrite the equation as follows...

 

(2/5 * x) + (5/5 * x) = 56  (remember that 5/5 = 1)

 

Adding the fractions (combine the numerators since the denominator of 5 is the same for both)...

 

7/5 * x = 56

 

To isolate the unknown "x", you multiply both sides of the equation by the reciprocal of 7/5 (which is 5/7)...

 

x = 56 * 5/7 = Your answer

 

Hope this helps!

 

 

Answer 3