The smallest county is 129 square miles large.
Step-by-step explanation:
Let,
Smallest county = x
Largest county = y
According to given statement;
The largest county in the state of Texas is 6064 square miles larger than the smallest county in the same state.
y = x+6064 Eqn 1
The size of the largest county is 48 times the size of the smallest county plus one square mile.
y = 48x+1 Eqn 2
As Eqn 1 and Eqn 2 are both equal to y, therefore,
Eqn 1 = Eqn 2
[tex]x+6064=48x+1\\6064-1=48x-x\\6063=47x\\47x=6063[/tex]
Dividing both sides by 47
[tex]\frac{47x}{47}=\frac{6063}{47}\\x=129\ square \ miles[/tex]
The smallest county is 129 square miles large.
Keywords: linear equation, substitution method
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