Question

One jug of powdered plant food treats an area of 140 square feet of flowers. How many jugs would be needed to treat an area of 175 square feet?

Use a graph plz!

Answer 1

Explanation:

Let
`n` and
`A` the number of jugs and the area of flowers, measured in jugs and square feet. We assume that exists a direct relationship between both variables. That is:

`A \propto n`

`A = k\cdot n` (1)

Where
`k` is the proportionality constant, measured in square feet per jug.

If we know that
`n = 1\,jug` and
`A = 140\,ft^(2)`, then the proportionality constant is:

`k = (A)/(n)`

`k = 140\,(ft^(2))/(jug)`

Then, the relationship between both variables is represented by:

`A = 140\cdot n`

If we know that
`A = 175\,ft^(2)`, then the minimum number of jugs needed to treat the area is:

`n = (175\,ft^(2))/(140\,(ft^(2))/(jug) )`

`n = 1.25\,jugs`

Since jugs represents a discrete set, then we round this number up to the next integer. In other words, we find that 2 jugs are needed to treat an area of 175 square feet.

Lastly, we present a graph to estimate the minimum value of jugs: