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SUBDIVISIONS
publish date: 2024/05/29 21:23:00 UTC
A developer donated to the county 100 of the 1,000 acres of land she owned. She divided the remaining acreage into \(1\frac13\)-acre lots. How many lots were created?
Correct Answer
$675$
Explanation
First, calculate the number of acres remaining after the donation:
$1000 \text{ acres} −100 \text{ acres} = 900 \text{ acres}$
Next, convert the size of each lot from a mixed number to an improper fraction:
$1\frac13 = \frac43$
Now, we need to determine how many \(1\frac13\)-acre lots can fit into the remaining 900 acres. This requires dividing the total remaining acres by the size of each lot:
$900 ÷ \frac43$
To perform the division, multiply by the reciprocal of the fraction:
$= 900 \cdot \frac34$
Calculate the multiplication and simplify:
$\require{cancel} = \frac{2700}{4} = \frac{27 \cdot 25 \cdot 4}{4} $
$= \frac{27 \cdot 25 \cdot \cancel{4}^1}{\cancel{4}_1} = 675$
Thus, the number of \(1\frac13\)-acre lots created is:
Reference
Mathematics for college students, go-math-science.com