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?

60% of what equals 27? This is the question. "Of" always means multiply.

So... convert the percent to a decimal: .6x=27.

Divide: x=27/.6
x=45

Plug it back in to check: .6(45)=27
27=27.

Or: 27/45=.6
.6=.6

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JonHenderson55 JonHenderson55 · Answer 2 · 2017-04-05T23:36:02+02:00

The answer is: "45" . Samuel has a total number of 45 cars.
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Explanation:
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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.
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Method 1)
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60% * x = 27 .

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

(0.6) x = 27 ;
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Divide EACH side by "(0.6)" ; to isolate "x" on one side of the equation; and to solve for "x" ;
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(0.6)x / (0.6) = 27/ 0.6 ;

x = 45 .
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Method 2)
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60% of x = 27 ;

(60/100) * x = 27;

Multiply BOTH SIDES of the equation by "100", to get rid of the fraction:
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100* { (60/100) x = 27 } ;

To get: 60x = 2700 ;
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Divide EACH side by "60" ; to isolate "x" on one side of the equation; and to solve for "x" ;
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60x / 60 = 2700/60 ;

x = 270/6 ;

x = 45 ;
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Method 3)
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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 .
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Method 4) Variant of "Method 3" above:
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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":
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60x 100 * 27
_____=____________ ;
60 60

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  x 100 * 27    5 * 5 * 3 * 3 * 3 * 2 * 2
__   =   ________  = __________________ ;
1    60   5 * 3 * 2 * 2
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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.
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We are left with:
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x   5 * 3 * 3
__   =     _______ = 5 * 3 * 3 = 45 . The answer is: x = 45 .
1      1

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