Question

Lisa's pet shop has 2 fish tanks. Tank A contains smaller fish who are fed 1 gram of food each per day. Tank B contains larger fish who are fed 2 grams of food each per day. If Tank B contains 2/3 the number of fish that Tank A contains, will Lisa ever feed both tanks the same amount of food? How many of each type of fish of fish would she need to have?

Answer 1

For A. 1/3 
For B. 2/3

Answer 2

Answer:

in tank A, we need 1 gram of food per fish.

In tank B, we need 2 gramms of food per fish.

If Na is the number of fish in tank A and Nb is the number of fish in tank B.

Then, the amount of food that the tank A needs is:

Na*1g of food

The tank B needs:

Nb*2g of food

And we know that Nb = 2/3*Na

we can replace it and get:

2/3*Na*2g

Then if both tanks need the same amount of food, we should have that both of these equations are equal:

food of tank A = food of tank B

Na*1g = (2/3)*Na*2g

we solve this for Na

Na = (2/3)*Na*2g/1g = (2/3)*Na*2 = (4/3)*Na

Na = (4/3)*Na

This equation has no solution, and from here we can conclude that if Nb = 2/3*Na, she will never give the same amount of food to both tanks.

b) knowing that the amount of food neded in tank A is half the amount for tank B, then we need the doulbe of fish in the tank A than in the tank B

Na = 2*Nb