Question

5/4 gallons of water fill 5/6 of a bucket how many gallons of water fill the entire bucket

Answer 1

`(3)/(2)` gallons

Explanation:

If
`(5)/(4)` gallons fill
`(5)/(6)` of a bucket.

Then we can write the ratio;

`(5)/(4):(5)/(6)`

Let
`x` gallons fill the entire bucket which is equivalent to
`1`.

Then we can again write the ratio;

`x:1`

We can write the following equation of proportion to solve for
`x`.

`(5)/(4):(5)/(6)=x:1`

This implies that;

`((5)/(4) )/((5)/(6) )=(x)/(1)`

We simplify to get;

`(5)/(4)* (6)/(5) }=x`

`x=(6)/(4) =(3)/(2)`

Therefore
`(3)/(2)` gallons will fill the entire bucket