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24 boys, 18 girls is the answer
Let x = boys and y = girls
3/4 x + 2/3 y = 30
x + y = 42 or x = 42-y
3/4 (42-y) + 2/3 y = 30
Solve for y:
126/4 - 3/4y + 2/3y = 30
-3/4y + 2/3 y = 120/4 -126/4
Get a common denominator
-9/12 y + 8/12y = -6/4
-1/12y = -6/4
-1/12y = -18/12
y = 18; x= 24
Let x = boys and y = girls
3/4 x + 2/3 y = 30
x + y = 42 or x = 42-y
3/4 (42-y) + 2/3 y = 30
Solve for y:
126/4 - 3/4y + 2/3y = 30
-3/4y + 2/3 y = 120/4 -126/4
Get a common denominator
-9/12 y + 8/12y = -6/4
-1/12y = -6/4
-1/12y = -18/12
y = 18; x= 24
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