Answer:
A) She should buy the
Step-by-step explanation:
Part A:
For question A, we find the areas of both plots and see which one is greater.
For the first one, we do 3/8 * 2/3
[tex]\frac{3}{8} * \frac{2}{3} = \frac{6}{24} = \frac{1}{4}[/tex]
The area of the first plot is 1/4 square miles
For the second one, we do 2/5 * 2/5
[tex]\frac{2}{5} *\frac{2}{5} = \frac{4}{25}[/tex]
The area of the second plot is 4/25 square miles
We have 1/4 and 4/25.
To see which one is bigger, we make them have the same denominator, also known as the LCM (Least Common Multiple).
LCM(4,25) = 100
Now we make 1/4 have a denominator of 100
4 times what is 100?
25, so the numerator is 25 and the denominator is 100.
We get: 25/100
Now we make 4/25 have a denominator of 100
25 times what is 100?
4, so the numerator is 4 * 4 = 16 and the denominator is 100.
We get: 16/100
Now we can see which is bigger:
25/100 or 16/100
25/100 is bigger
Therefore, Miguel's mother should buy the plot with dimensions 3/8 and 2/3.
Part B
For part B, I'm not sure which plot of land she is going to pay for, so I will answer both.
We answered this in Part A already.
The 3/8 and 2/3 plot was 1/4 square miles and the 2/5 by 2/5 plot was 4/25 square miles.
Plot 1:
1/4 square miles
It said that it costs $750,000 for a square mile
This plot is 1/4 square miles, so we do
[tex]$750,000 * \frac{1}{4} = \frac{750,000}{4} = 187,500[/tex]
The cost for plot 1 is $187,500
Plot 2:
4/25 square miles
It said that it costs $750,000 for a square mile
This plot is 4/25 square miles, so we do
[tex]750,000*\frac{4}{25} = \frac{3,000,000}{25} = 120,000[/tex]
The cost for plot 1 is $120,000
So for the 3/8 by 2/3 plot, it cost $187,500 and for the 2/5 by 2/5 plot costs $120,000
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