Solve 160/250x/200+x=40/140

$$\frac { \frac { 160 } { 250 } x } { 200 + x } = \frac { 40 } { 140 }$$

Solve for x

$$x = \frac{5000}{31} = 161\frac{9}{31} \approx 161.290322581$$

Steps for Solving Linear Equation

Variable x cannot be equal to -200 since division by zero is not defined. Multiply both sides of the equation by 140\left(x+200\right), the least common multiple of 200+x,140.

$$140\times \frac{160}{250}x=\left(x+200\right)\times 40$$

Reduce the fraction \frac{160}{250} to lowest terms by extracting and canceling out 10.

$$140\times \frac{16}{25}x=\left(x+200\right)\times 40$$

Multiply 140 and \frac{16}{25} to get \frac{448}{5}.

$$\frac{448}{5}x=\left(x+200\right)\times 40$$

Use the distributive property to multiply x+200 by 40.

$$\frac{448}{5}x=40x+8000$$

Subtract 40x from both sides.

$$\frac{448}{5}x-40x=8000$$

Combine \frac{448}{5}x and -40x to get \frac{248}{5}x.

$$\frac{248}{5}x=8000$$

Multiply both sides by \frac{5}{248}, the reciprocal of \frac{248}{5}.

$$x=8000\times \frac{5}{248}$$

Multiply 8000 and \frac{5}{248} to get \frac{5000}{31}.

$$x=\frac{5000}{31}$$