Question

A bag of 3 lb of Fairlawn's Number 25 grass seed covers a 4000 ft area. How great an area will 16 oz of the same seed cover?

Answer 1

`16oz=1lb" covers "1333 1/3 ft^2`

Explanation:

`color(blue)("Shortcut method")`

Note that `16 oz=1lb`

`"area for "1lb" of seed" = color(red)(4000ft^2-:3) = 1333 1/3 ft^2`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(red)("This is why the shortcut method works")`

`color(blue)("First principle method")`

Note that `16 oz=1lb`

Using ratios in fraction format. We are after area so we put that at the top (numerator).

Initial condition: `" "("area")/("weight of seed") ->(4000ft^2)/(3lb)`

But we need the area for `16oz=1lb`

Ratios always have the proportioning fixed so we can write:

`" "("area")/("weight of seed") ->(4000ft^2)/(3lb)-=("area")/(1lb)`

The `-=` means equivalent to.

To change `3lb` into `1lb` divide by 3. To maintain the correct proportion also divide the top (numerator) by 3 as well.

`" "("area")/("weight of seed") ->(4000ft^2)/(3lb)-=(color(red)(4000ft^2-:3))/(3lb-:3)=("area")/(1lb)`

So the area covered by `1lb` is `color(red)(4000ft^2-:3)= 1333 1/3ft^2`