Question

Assume that the amount of water that Mario uses for irrigation at his vineyard in inversely proportional to the amount of rainfall. if he uses 40,000 gallons during a month in which there is 6" of rain, how much water would be used in a month that has 7" of rain? (round to nearest integer as needed)

Answer 1

34,286 gallons

Explanations:

Let the amount of water that Mario uses for irrigation be A

Let the amount of rainfall be "r"

If the amount of water that Mario uses for irrigation at his vineyard in inversely proportional to the amount of rainfall, this is expressed as:

`\begin{gathered} A\alpha(1)/(r) \\ A=(k)/(r) \end{gathered}`

If he uses 40,000 gallons during a month in which there is 6" of rain, this means that A = 40,000 and r = 6"

Substitute the given values into the formula:

`\begin{gathered} 40,000=(k)/(6) \\ k=6*40,000 \\ k=240,000 \end{gathered}`

In order to know how much water would be used in a month that has 7" of rain, this means that;

A = ?, r = 7"

Get the value of "A"

Recall that:

`\begin{gathered} A=(k)/(r) \\ A=(240,000)/(7) \\ A=34,285.7 \end{gathered}`

This shows that about 34,286 gallons of water would be used in a month that has 7" of rain.