Samuel has a collection of toy cars. his favorites are the 27 red ones which make up 60 % of his collection. how many toy cars does samuel have?

The answer is:  "45" .   Samuel has a total number of 45 cars. 

Explanation:

Let "x" represent the total number of cars in the ENTIRE collection.

Let "y" = number of red cars = 27.

27 cars, or "y", make up 60% of the entire collection, or "x":

27 = 60% * x .   Solve for "x", which is our answer.

Method 1)


60% * x = 27 .

60/100 * x = 27 ;   60/100 = 0.60 = 0.6;

(0.6) x = 27 ; 

Divide EACH side by "(0.6)" ; to isolate "x" on one side of the equation; and to solve for "x" ; 

(0.6)x / (0.6) = 27/ 0.6 ; 

                x = 45 .

Method 2)

 60% of x = 27 ;

(60/100) * x = 27;

 Multiply BOTH SIDES of the equation by "100", to get rid of the fraction:

 100* { (60/100) x = 27 } ;

To get:  60x  = 2700 ;

Divide EACH side by "60" ; to isolate "x" on one side of the equation; and to solve for "x" ;

       60x / 60  = 2700/60 ;
              
          x  = 270/6 ; 
          
          x = 45 ;

Method 3)

60% of x = 27 ; 

(60/100)x = 27; 

(60x) / 100  = 27 ;

Multiply EACH side of the equation by "100" :

60x = 100 * 27 ;

60x = 2700; 

Divide each side of the equation by "60" ; 

60x/60 =2700/60 ; to get x = 45 .

Method 4) Variant of "Method 3" above:


60% of x = 27 ; 

(60/100)x = 27; 

(60x) / 100  = 27 ;

Multiply EACH side of the equation by "100" :

60x = 100 * 27 ;

Divide each side by "60", to isolate "x" on one side of the equation; and to solve for "x":


60x           100 * 27
=   ; 
60               60                                                  



  x          100 * 27          5 * 5 * 3 * 3 * 3 * 2 * 2
 __   =     =      ;
  1             60                         5 * 3 * 2 * 2                         


     Cancel out 2 (TWO) "2's from the top; and BOTH "2's from the bottom; and the "5" AND the 3" from the bottom";  and 1 (ONE) of the "5's) from the top;  and 1 (ONE) of the "3"s" from the top.
    The bottom half of this fraction is eliminated completely, since the bottom half equals "1";  and any value—including the entire value of the "top half"; divided by "1"— equals that same value.

   We are left with:


  x           5 * 3 * 3
 __   =      =  5 * 3 * 3  = 45 .   The answer is:  x = 45 .
  1                1 

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