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Answer: B) 1,800 acres</h3>
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Explanation:
Let
r = area devoted to residential use
This variable is some positive real number, and it represents the area in acres.
Your teacher says that " the area devoted to business use is 7,200 acres less than the area devoted to residential use"
This means the expression r-7200 represents the area for business use
Note the jump from 25% to 65% is 65/25 = 2.6, meaning that we multiply by 2.6 when going from the business area to the residential area.
So we'll multiply by 2.6 to go from r-7200 to r
We'll have this equation
2.6(r-7200) = r
because it's effectively saying
2.6*(business area) = residential area
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Let's isolate r
2.6(r-7200) = r
2.6r-2.6*7200 = r
2.6r - 18720 = r
2.6r - r = 18720
1.6r = 18720
r = 18720/(1.6)
r = 11700
We'll use 11700 acres for the residential portion.
And also r-7200 = 11700-7200 = 4500 acres are set aside for the business district.
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The largest region (residential) uses 11700 acres of land.
Note the jump from 10% to 65% involves a multiplier of 6.5 because 65/10 = 6.5
So if g is the amount of government land used, then,
6.5g = r
6.5g = 11700
g = 11700/(6.5)
g = 1800
1800 acres of land are for government use
This is why the answer is choice B.
