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<span> . </span>______________________________________________ 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": ___________________________________________
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