Solve 101+x/168+x=0.618

$$\frac{ 101+x }{ 168+x } = 0.618$$

Solve for x

$$x = \frac{1412}{191} = 7\frac{75}{191} \approx 7.392670157$$

Steps for Solving Linear Equation

Variable x cannot be equal to -168 since division by zero is not defined. Multiply both sides of the equation by x+168.

$$101+x=0.618\left(x+168\right)$$

Use the distributive property to multiply 0.618 by x+168.

$$101+x=0.618x+103.824$$

Subtract 0.618x from both sides.

$$101+x-0.618x=103.824$$

Combine x and -0.618x to get 0.382x.

$$101+0.382x=103.824$$

Subtract 101 from both sides.

$$0.382x=103.824-101$$

Subtract 101 from 103.824 to get 2.824.

$$0.382x=2.824$$

Divide both sides by 0.382.

$$x=\frac{2.824}{0.382}$$

Expand \frac{2.824}{0.382} by multiplying both numerator and the denominator by 1000.

$$x=\frac{2824}{382}$$

Reduce the fraction \frac{2824}{382} to lowest terms by extracting and canceling out 2.

$$x=\frac{1412}{191}$$