Solve for x
x=100
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\frac{180+x}{600+x}=\frac{40}{100}
Divide both sides by 100.
\frac{180+x}{600+x}=\frac{2}{5}
Reduce the fraction \frac{40}{100} to lowest terms by extracting and canceling out 20.
5\left(180+x\right)=2\left(x+600\right)
Variable x cannot be equal to -600 since division by zero is not defined. Multiply both sides of the equation by 5\left(x+600\right), the least common multiple of 600+x,5.
900+5x=2\left(x+600\right)
Use the distributive property to multiply 5 by 180+x.
900+5x=2x+1200
Use the distributive property to multiply 2 by x+600.
900+5x-2x=1200
Subtract 2x from both sides.
900+3x=1200
Combine 5x and -2x to get 3x.
3x=1200-900
Subtract 900 from both sides.
3x=300
Subtract 900 from 1200 to get 300.
x=\frac{300}{3}
Divide both sides by 3.
x=100
Divide 300 by 3 to get 100.
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