ratio and proportion

Question

In Fairy Tale Day School, 25% of students are sixth graders. 48% of sixth graders are girls. 60% of sixth grade girls dressed up as Elsa for the school's costume party.

If 36 sixth grade girls dressed up as Elsa, what is the total enrollment of Fairy Tale Day School?

Answer 1

This is a multi-step equation.   We know that 25% of all students are 6th graders, 48% of those 6th graders are girls, and 60% of those girls dressed up as Elsa.   Starting from the end and working back, we can solve 3 different proportions to find the total enrollment. 

 

To find the number of 6th grade girls:

 

60/100 = 36/x   ( 60 is the percent of girls who dressed as Elsa = 36 girls who dressed as Elsa)

60x = 3600       (Find the cross products and divide by 60)

    x = 60 sixth grade girls  

 

To find the number of 6th graders in all, use the number of 6th grade girls you just found in the proportion below. 

 

48/100 = 60/x

48x = 6000

x = 125 sixth graders in all

 

Finally, to find the total enrollment of the school, use the number of 6th graders you found in the proportion below.

 

25/100 = 125/x

25x = 12,500

x = 500 students enrolled at Fairy Tale Day School.