Solve 96+x/160+x=0.618

$$\frac{ 96+x }{ 160+x } =0.618$$

Solve for x

$$x = \frac{1440}{191} = 7\frac{103}{191} \approx 7.539267016$$

Steps for Solving Linear Equation

Variable x cannot be equal to -160 since division by zero is not defined. Multiply both sides of the equation by x+160.

$$96+x=0.618\left(x+160\right)$$

Use the distributive property to multiply 0.618 by x+160.

$$96+x=0.618x+98.88$$

Subtract 0.618x from both sides.

$$96+x-0.618x=98.88$$

Combine x and -0.618x to get 0.382x.

$$96+0.382x=98.88$$

Subtract 96 from both sides.

$$0.382x=98.88-96$$

Subtract 96 from 98.88 to get 2.88.

$$0.382x=2.88$$

Divide both sides by 0.382.

$$x=\frac{2.88}{0.382}$$

Expand \frac{2.88}{0.382} by multiplying both numerator and the denominator by 1000.

$$x=\frac{2880}{382}$$

Reduce the fraction \frac{2880}{382} to lowest terms by extracting and canceling out 2.

$$x=\frac{1440}{191}$$