Solve for \(x\) in \(\frac{6x}{75}+\frac{20000-x}{75}=800\).
Solve for \(x\).
\[\frac{6x}{75}+\frac{20000-x}{75}=800\]
Simplify \(\frac{6x}{75}\) to \(\frac{2x}{25}\).
\[\frac{2x}{25}+\frac{20000-x}{75}=800\]
Simplify using the common denominator.
\[\frac{2\times 3x+20000-x}{75}=800\]
Simplify \(2\times 3x\) to \(6x\).
\[\frac{6x+20000-x}{75}=800\]
Simplify \(6x+20000-x\) to \(5x+20000\).
\[\frac{5x+20000}{75}=800\]
Factor out the common term \(5\).
\[\frac{5(x+4000)}{75}=800\]
Simplify \(\frac{5(x+4000)}{75}\) to \(\frac{x+4000}{15}\).
\[\frac{x+4000}{15}=800\]
Multiply both sides by \(15\).
\[x+4000=800\times 15\]
Simplify \(800\times 15\) to \(12000\).
\[x+4000=12000\]
Subtract \(4000\) from both sides.
\[x=12000-4000\]
Simplify \(12000-4000\) to \(8000\).
\[x=8000\]
Substitute \(x=8000\) into \(-8dotx\times 100+20000-x\times 75=800\).
Start with the original equation.
\[-8dotx\times 100+20000-x\times 75=800\]
Let \(x=8000\).
\[-8dot\times 8000\times 100+20000-8000\times 75=800\]
Simplify.
\[-6400000dot-580000=800\]
Substitute \(x=8000\) into \(\frac{6x-x+20000}{75}=800\).
Start with the original equation.
\[\frac{6x-x+20000}{75}=800\]
Let \(x=8000\).
\[\frac{6\times 8000-8000+20000}{75}=800\]
Simplify.
\[800=800\]
Since \(800=800\) is redundant information, this is a dependent system.
