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A construction company is preparing 10 acres of land for a new housing community. The land contains large rocks that need to be removed. A machine removes 10 rocks from 360 square feet of land. If the rocks are distributed evenly, how many rocks are there on all 10 acres?

Note: 1 acre = 43,560 square feet.

Answer :

Sure! Let's solve the problem step-by-step.

1. Determine how many square feet are in one acre:
We know that 1 acre equals 43,560 square feet.

2. Calculate the total square feet for 10 acres:
Since there are 43,560 square feet in one acre, for 10 acres, you multiply:
[tex]\[
10 \times 43,560 = 435,600 \text{ square feet}
\][/tex]

3. Understand how rocks are distributed:
It is given that a machine removes 10 rocks from every 360 square feet of land.

4. Calculate the number of rocks for 435,600 square feet:
First, we calculate how many 360-square-foot sections are there in 435,600 square feet:
[tex]\[
\frac{435,600}{360} = 1,210
\][/tex]

5. Calculate the total number of rocks:
Since each section of 360 square feet contains 10 rocks, we multiply:
[tex]\[
1,210 \times 10 = 12,100
\][/tex]

Therefore, there are 12,100 rocks on all 10 acres.

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