Fraction word problem

Question

A large school of small fish was swimming in he ocean. A shark came and ate 2/3 of the fish. Then a group of seals ate half of the remaining fish. 7 of those fish were eaten by a larger fish. Of the fish that were left, 3/4 got caught in a net. Now there are 9 small fish left.  How many fish were there to start with?

Answer 1

Let f = # of fish we began with.

 

A shark ate 2/3 of f.  what remained was 1/3 of f.

 

A seal ate 1/2 of the remaining fish.  The seal ate 1/2 of 1/3 of f = 1/6 of f.

So what remains is 1/6 of f ..... note: ... 1/6 + 1/6 = 2/6 = 1/3

 

7 of the remainder were eaten by a larger fish.

That leaves us with (1/6)f - 7

 

Of that remainder, 3/4 of those were caught in a net.

That means that 1/4 of [(1/6)f - 7] remain .... which is 9.

 

So our equation is:

     

    (1/4)[(1/6)f - 7] = 9

 

Multiplying both sides by 4,

 

     (1/6)f - 7 = 36

 

Multiplying both sides by 6,

 

     f - 42 = 1512

     f = 1512 + 42

     f = 1554