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In my fencing club there are twice as many boys who are in high school as there are boys who are in middle school. Of the students in the club who are in middle school, there are three times as many girls as there are boys. Half of the girls who are in the club are in high school. Everyone in my fencing club is in either middle school or high school. If there are 72 people in my fencing club, how many are middle school boys?

Guest Feb 20, 2015

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 #1
avatar+81051 
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In my fencing club there are twice as many boys who are in high school as there are boys who are in middle school. Of the students in the club who are in middle school, there are three times as many girls as there are boys. Half of the girls who are in the club are in high school. Everyone in my fencing club is in either middle school or high school. If there are 72 people in my fencing club, how many are middle school boys?

x = boys in middle school ....    2x =  boys in high school .... girls in middle school = 3x  = girls in high school

So we have

x + 2x + 3x + 3x = 72    combine like terms

9x = 72    divide by 9 on both sides

x = 8   this is the number of boys in middle school

 

CPhill  Feb 20, 2015
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 #1
avatar+81051 
+5
Best Answer

In my fencing club there are twice as many boys who are in high school as there are boys who are in middle school. Of the students in the club who are in middle school, there are three times as many girls as there are boys. Half of the girls who are in the club are in high school. Everyone in my fencing club is in either middle school or high school. If there are 72 people in my fencing club, how many are middle school boys?

x = boys in middle school ....    2x =  boys in high school .... girls in middle school = 3x  = girls in high school

So we have

x + 2x + 3x + 3x = 72    combine like terms

9x = 72    divide by 9 on both sides

x = 8   this is the number of boys in middle school

 

CPhill  Feb 20, 2015

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