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Sports participation in a class: Use ratios and non-participant difference to find girls in class. Total students = 60; participant ratio (boys : girls) = 3 : 2. Girls not participating are 5 more than boys not participating. If boys participating = 15, determine the total number of girls in the class. Choose the correct value.

Difficulty: Easy

Correct Answer: 30

Explanation:


Translate ratio to counts

  • Boys participating = 15 corresponds to the “3” part ⇒ 3k = 15 ⇒ k = 5.
  • Girls participating = 2k = 10.


Non-participants relationship
Let total boys = B, girls = G (B + G = 60).Girls not participating = G − 10; boys not participating = B − 15.Given: G − 10 = (B − 15) + 5 ⇒ G = B.


Compute totals
If G = B and B + G = 60 ⇒ B = G = 30.


Final Answer
30

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