What is the largest county in the state of texas

Asked by admin @ 28/10/2021 in Mathematics viewed by 332 People

The largest county in the state of Texas is 6064 square miles larger than the smallest county in the same state. The size of the largest county is 48 times the size of the smallest county plus one square mile. How large is the smallest county in the state of Texas ?

Answered by admin @ 28/10/2021

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

$x+6064=48x+1\\6064-1=48x-x\\6063=47x\\47x=6063$

Dividing both sides by 47

$\frac{47x}{47}=\frac{6063}{47}\\x=129\ square \ miles$

The smallest county is 129 square miles large.

Keywords: linear equation, substitution method

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