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?

1 Answer
Dec 17, 2016

Answer:

#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#

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#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#