Fraction questions

Question

At a school swimming meet, 1/3 of the pupils were boys. Given that 2/5 of the boys and 3/5 of the girls did not know how to swim, how many pupils were there altogether if there were 490 swimmers a the swimming meet?

Answer 1

Let s = total # students

b = # boys

g = # girls

 

s = b+g

(1/3)s = b

(2/5)b + (3/5)g did not know how to swim

 

(3/5)b + (2/5)g = 490 swimmers

 

(1/3)(b+g) = b

b + g = 3b

2b = g

b = g/2

 

(3/5)(g/2) + (2g/5) = 490

3g/10 + 4g/10 = 490

7g/10 = 490

g = 490(10/7) = 700 girls

 

b = g/2 = 350 boys

 

total pupils = 1050