Respuesta :
Yes, the population of Town C increased by at least 100 percent from the year 2000 to the year 2010
Statement 1: The population of Town C in 2000 was 2/3 of the population in 2005
This tells us the population change from 2000 to 2005 since we need to know the population change from 2000 to 2010, this statement is not sufficient.
Statement 2: The population of Town C increased by a greater number of people from 2005 to 2010 than it did from 2000 to 2005.
Since statement 2 provides no information about the population change from 2000 to 2005, there is no to answer this question with certainty. thus, statement 2 is not sufficient
Statement 1 and Statement 2 combined:
Let X= the population in 2000
Let Y= the population in 2005
Let Z= the population in 2010
From statement 1, we can write: X=[tex]\frac{2}{3}[/tex]Y
Multiply both sides by 3 to get [tex]3X=2Y[/tex]
Divide both sides by 2 to get [tex]\frac{3}{2}X=Y[/tex]
=>[tex]Y=1.5X[/tex]
As per statement 2, let's first determine the increase in the number of people from 2000 to 2005
If [tex]Y=1.5X[/tex], we know
X= the population in 2000
1.5X= the population in 2005
[tex]1.5X-X=0.5X[/tex]
So, the population increased [tex]0.5X[/tex] from 2000 to 2005
So, from 2005 to 2010, the population increased at least 0.5X
1.5X= the population in 2005
[tex]1.5X+0.5X=2.0X[/tex]
So, the population in 2010 was at least 2.0X
In other words, the population at least doubled from 2000 to 2010
So, the answer to the target question is yes, the population of Town C increased by at least 100 percent from the year 2000 to the year 2010
Did the population of Town C increase by at least 100 percent from the year 2000 to the year 2010?
(1) The population of Town C in 2000 was 2/3 of the population in 2005.
(2) The population of Town C increased by a greater number of people from 2005 to 2010 than it did from 2000 to 2005.
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