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?

Dec 17, 2016

$16 o z = 1 l b \text{ covers } 1333 \frac{1}{3} f {t}^{2}$

Explanation:

$\textcolor{b l u e}{\text{Shortcut method}}$

Note that $16 o z = 1 l b$

$\text{area for "1lb" of seed} = \textcolor{red}{4000 f {t}^{2} \div 3} = 1333 \frac{1}{3} f {t}^{2}$

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$\textcolor{red}{\text{This is why the shortcut method works}}$

$\textcolor{b l u e}{\text{First principle method}}$

Note that $16 o z = 1 l b$

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 $16 o z = 1 l b$

Ratios always have the proportioning fixed so we can write:

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

The $\equiv$ means equivalent to.

To change $3 l b$ into $1 l b$ 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 $1 l b$ is $\textcolor{red}{4000 f {t}^{2} \div 3} = 1333 \frac{1}{3} f {t}^{2}$