Answer:
Number of black counters = 5
Step-by-step explanation:
Let,
x be the total number of counters
Number of red counters = [tex]\frac{1}{3}x[/tex]
Number of black counters = [tex]\frac{1}{6}x[/tex]
Number of green counters = 15
Now,
Red counters + Black counters + Green counters = Total counters
[tex]\frac{1}{3}x+\frac{1}{6}x+15=x\\\\\frac{2x+x+90}{6}=x\\\\3x+90 = 6x\\90 = 6x-3x \\90 = 3x\\3x = 90[/tex]
Dividing both sides by 3
[tex]\frac{3x}{3}=\frac{90}{3}\\x=30[/tex]
Number of black counters = [tex]\frac{1}{6}*30[/tex] = 5
Hence,
Number of black counters = 5
