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avatar+206 

Every student in the school math club is either in 7th th or 8th grade, and either has blue, green, or brown eyes. There are 46 students in the math club. Of these students, 9 students are 7th graders with blue eyes,  9 students are 8th graders with brown eyes, and a total of 9 students have  green eyes. There are three times as many 7th graders as there are students with blue eyes, and twice as many students with brown eyes as there are 8th graders. How many students in the math club are 7th graders with green eyes


So i made a table with all the values that i did know and thats all i understand

 Aug 2, 2022
 #1
avatar+2437 
0

Make a table and fill it in with variables.  

 

                blue eyes        brown eyes       green eyes

7th-grade       9                        a                        b

 

8th-grade        c                        9                       d

 

We have the following equations, and we need to solve for b: 

 

\(9 = b + d \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (i)\)

\(9 + a + b = 3(9 + c) \ \ \ \ \ \ \ \ \ \ \ (ii)\)

\(9 + a = 2(9 + c + d) \ \ \ \ \ \ \ \ \ \ \ (iii)\)

\(18 + a + b + c + d = 46 \ \ \ \ \ \ (iv)\)

 

After solving for b, we find \(b = \color{brown}\boxed{7}\)

 Aug 3, 2022
 #2
avatar+113 
+1

I hope You can take it from there.

 Aug 3, 2022

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