Question

The ratio of boys to girls at King Middle school is 3:2. What is the ratio of girls to all students?

Answer 1

The answer is:  " 2 :5 " ;  or, write as:  " 2/5 " . 
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The ratio of 'girls' to 'all students' is:  "2: 5 " ;  or, write as:  " 2/5 ".
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Explanation:
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Given:  The ratio of boys to girls is:  " 3:2 " .  

Problem:  Find the ratio of "girls" to "all students:
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Note:    This ratio of "boys to girls", which is " 3 : 2 " ; 
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    →  can be expressed as " 3x: 2x"  ;  

in which the total number of students is:  " 3x + 2x " = 5x " .

   → The total number of students is represented as:  " 5x " .  
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→  The ratio of "girls to boys" is:  "2x : 3x" .

→  {that is;  the "inverse" of the ratio of "boys to girls"} ;  
→  {that is;  the "inverse" of  " 3x: 2x" } ;  →  which is:  " 2x : 3x " .
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The ratio of "girls" to "all students" is:  "2x : 5x "  ;  or " 2x/5x " ; 
                                             → Both "x" values cancel ;  {since: " x/x = 1 "} ; 
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       →  and we have the answer:  " 2 :5 " ;  or, write as:  " 2/5 " . 
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The ratio of 'girls' to 'all students' is:  " 2 :5 " ;  or, write as:  " 2/5 ".
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