Question

James left a bin in his garden to collect rainwater. He notices that 1/4 gallon of water fills 2/3 of the bin. Write an equation to find the amount of water that will fill the entire bin.

Answer 1

We are given in the question that:

`(1)/(4)\text{ gallon}=(2)/(3)\text{ bin}`

We are meant to calculate the number of gallons that will fill the entire bin, such that we can have:

`x\text{ gallons}=1\text{ bin}`

We know that the ratio of both expressions will give the same value, therefore, the equation that can be used to solve will be:

`((1)/(4))/((2)/(3))=(x)/(1)`

We can further solve to get the amount of water by cross-multiplying:

`\begin{gathered} (1)/(4)*1=(2)/(3)* x \\ (1)/(4)=(2)/(3)x \end{gathered}`

Solving, we have:

`\begin{gathered} 2x*4=3*1 \\ 8x=3 \\ x=(3)/(8) \end{gathered}`

Therefore, it will take 3/8 gallons to fill the bin.