Please solve

Question

Three fifths of a number added to one fourth of the number is 51 Find the number.

Answer 1

Let the number =X    

 

This Gives us      (3)X + (1)X = 51

                          5         4

 

Now we find the lowest common denominator of 5 and 4, which is 20.  (Both 5 and 4 are evenly divisible by 20.)

 

We obtain common denominators for our fractions as follows:   (4*3)X  +  (5*1)X  =  51

                                                                                             4*5           5*4                                                   

And    12X  +  5X  =  51

          20        20                                   

          

 

Adding our fractions, we get   12X + 5X = 51  and  17X = 51

                                             20                          20

       

 

We next multiply both sides of our equation by 20 to eliminate our denominator:

 

20(17X) = 20(51)

    20

 

And   17X = 1020

 

Dividing both sides of the equation by 17 gives us  X = 1020

                                                                                  17

                                                                              

And X = 60

 

Proof

 

3(60) + 1(60) = 51

   5          4

 

180 + 60  = 51

  5       4

 

 36 + 12 = 51

Answer 2

So think of it as 3/5 n + 1/4 n = 51, but since you have different denominators, you can't add them easily.

 

let's find a common denominator so they can "speak the same language." A good common denominator here is 20, since both denominators are factors of 20.

 

So 3/5 is the same as 12/20, and 1/4 is the same as 5/20.

 

so 12/20n + 5/20n = 51, so 17/20 x n = 51.

 

Get rid of that pesky fraction by multiplying both sides by 20:

 

17n = 1020. then divide each side by 17 to give you:

 

n = 60.

 

there ya go!