A rather large fish tank has a practical fill volme of 36 3/4 cubic feet. If a cubic foot of water represents 7 1/2 gallons of water

Question

Two questions;

 

A.  How many gallons will the tank hold?

B. Assuming the tank weighs 50 pounds empty and water weighs 8 1/3 pounds per gallon, how much will the filled tank weigh before you add the fish?

 

 

Answer 1

It will be easy to type if we convert to decimal for now, and so we'll put back into fractions at the end:

• Practical fill volume = 36.75 cubic feet
• 7.5 gallons of water per cubic foot

We can find the gallons of water the tank holds by maintaining ratio of 1:7.5 (cubic feet: gallons). We just need to multiply both parts of the ratio by the same factor of 36.75, which is the volume of water in cubic feet given.

 

1 cubic foot  =  x36.75  =  36.75 cubic feet

——————                      —————————

7.5 gallons       x36.75       275.625 gallons

 

For every 36.75 cubic feet there are 275.625 gallons, or 275 5/8 gallons. (A)

 

For part (B), we set up similar work. Once we find what the water weighs, let's not forget to add the 50 pounds for the tank weight. We simply multiply how many gallons we have by the gallon to weight ratio given (Here, 8 1/3 ≈ 8.3333):

 

1 gallon     =  x275.625  =  275.625 gallons

—————                          —————————

8.3333 lbs      x275.625      2,296.875 lbs

 

So, in fractions, the 275 5/8 gallons of water weigh 2,296.875 or 2,296 7/8 lbs. Let's add the 50 lbs for the tank:

50 lbs + 2,296 7/8 lbs = 2,346 7/8 lbs. (B)