84 students took part in a Science contest. In Round A, the number of boys to the number of girls is 7:5. In Round B, some boys and girls were eliminated in the ratio of 1:2. At the end of Round C, the number of boys left was 5/3 of the number of girls. How many boys and girls were eliminated in Round B altogether?
Round A
boys : girls = 7:5 = 7x : 5x
7x + 5x = 84
12x = 84
x = 7
So there were 49 boys and 35 girls
Round B:
students gone:
boys : girls = y : 2y
round C
students left behind:
boys : girls = 49-y : 35-2y
49-y = (5/3)(35-2y)
147 - 3y = 175 - 10y
7y = 28
y = 4
Now everything is falling into place, look at my definitions
and state the answers to the final question.