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Answer :
Jill owns approximately 1.38 acres of land.
To find out how many acres of land Jill owns, we first need to determine the total number of peach trees on all her land.
Since she counts 150 peach trees on half of her land, we can assume there are 300 peach trees in total (since half of her land has 150 trees and the other half will also have 150 trees).
Now, if there are 5 trees for every 1,000 square feet of land, we can set up a proportion to find out how many square feet of land these 300 trees occupy:
[tex]\( \frac{5 \text{ trees}}{1000 \text{ square feet}} = \frac{300 \text{ trees}}{x \text{ square feet}} \)[/tex]
Cross-multiplying, we get:
[tex]\( 5x = 300,000 \)[/tex]
Dividing both sides by 5:
[tex]\( x = 60,000 \)[/tex]
So, Jill's 300 peach trees occupy 60,000 square feet of land.
To convert this to acres, we use the conversion factor provided: [tex]1 acre = 43,560 square feet.[/tex]
[tex]\( \text{Number of acres} = \frac{60000}{43560} \)[/tex]
[tex]\( \text{Number of acres} = 1.38 \)[/tex]
Complete correct question:
Jill counts 150 peach trees on 1/2 of the land she owns. She determines that there are 5 trees for every 1,000 square feet of land. About how many acres of land does Jill own? [tex]1 acre= 43,560 square feet.[/tex]
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Jill owns approximately 60,000 acres of land.
Let's first find out how many trees Jill has per acre based on the information given.
Jill has 150 peach trees on 1/2 of her land, which means she has 300 peach trees on her entire land. If there are 5 trees for every 1,000 square feet of land, we can calculate the total square feet of land that Jill owns:
[tex]\[ \text{Total trees} = \text{Trees per acre} \times \text{Total acres} \]\[ 300 = \frac{5}{1000} \times \text{Total acres} \][/tex]
Solving for the total acres:
[tex]\[ \text{Total acres} = \frac{300}{\frac{5}{1000}} \]\[ \text{Total acres} = \frac{300 \times 1000}{5} \]\[ \text{Total acres} = \frac{300000}{5} \]\[ \text{Total acres} = 60000 \][/tex]
Now, we can convert the total acres from square feet to acres using the conversion factor given:
[tex]\[ \text{Total acres in square feet} = 60000 \times 43560 \]\[ \text{Total acres} = \frac{60000 \times 43560}{43560} \]\[ \text{Total acres} = 60000 \][/tex]
So, Jill owns approximately 60,000 acres of land.
