Solve 96+x/163+x=0.618

$$\frac { 96 + x } { 163 + x } = 0.618$$

Solve for x

$$x = \frac{2367}{191} = 12\frac{75}{191} \approx 12.392670157$$

Steps for Solving Linear Equation

Variable x cannot be equal to -163 since division by zero is not defined. Multiply both sides of the equation by x+163.

$$96+x=0.618\left(x+163\right)$$

Use the distributive property to multiply 0.618 by x+163.

$$96+x=0.618x+100.734$$

Subtract 0.618x from both sides.

$$96+x-0.618x=100.734$$

Combine x and -0.618x to get 0.382x.

$$96+0.382x=100.734$$

Subtract 96 from both sides.

$$0.382x=100.734-96$$

Subtract 96 from 100.734 to get 4.734.

$$0.382x=4.734$$

Divide both sides by 0.382.

$$x=\frac{4.734}{0.382}$$

Expand \frac{4.734}{0.382} by multiplying both numerator and the denominator by 1000.

$$x=\frac{4734}{382}$$

Reduce the fraction \frac{4734}{382} to lowest terms by extracting and canceling out 2.

$$x=\frac{2367}{191}$$