Solve {l}{frac{{(x-18.164)}}{x}=0.3{(frac{25/1004-18164)}}{25949}}{y=x}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { \frac{{(x - 18.164)}}{x} = 0.3 \frac{{(\frac{25}{100} 4 - 18164)}}{25949} }\\ { y = x }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z = \frac{117834409}{7849475} = 15\frac{92284}{7849475} \approx 15.01175671$$

Solution Steps

Consider the first equation. Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 25949x, the least common multiple of x,25949.

$$25949\left(x-18.164\right)=0.3x\left(\frac{25}{100}\times 4-18164\right)$$

Use the distributive property to multiply 25949 by x-18.164.

$$25949x-471337.636=0.3x\left(\frac{25}{100}\times 4-18164\right)$$

Reduce the fraction \frac{25}{100} to lowest terms by extracting and canceling out 25.

$$25949x-471337.636=0.3x\left(\frac{1}{4}\times 4-18164\right)$$

Multiply \frac{1}{4} and 4 to get 1.

$$25949x-471337.636=0.3x\left(1-18164\right)$$

Subtract 18164 from 1 to get -18163.

$$25949x-471337.636=0.3x\left(-18163\right)$$

Multiply 0.3 and -18163 to get -5448.9.

$$25949x-471337.636=-5448.9x$$

Add 5448.9x to both sides.

$$25949x-471337.636+5448.9x=0$$

Combine 25949x and 5448.9x to get 31397.9x.

$$31397.9x-471337.636=0$$

Add 471337.636 to both sides. Anything plus zero gives itself.

$$31397.9x=471337.636$$

Divide both sides by 31397.9.

$$x=\frac{471337.636}{31397.9}$$

Expand \frac{471337.636}{31397.9} by multiplying both numerator and the denominator by 1000.

$$x=\frac{471337636}{31397900}$$

Reduce the fraction \frac{471337636}{31397900} to lowest terms by extracting and canceling out 4.

$$x=\frac{117834409}{7849475}$$

Consider the second equation. Insert the known values of variables into the equation.

$$y=\frac{117834409}{7849475}$$

Consider the third equation. Insert the known values of variables into the equation.

$$z=\frac{117834409}{7849475}$$

The system is now solved.

$$x=\frac{117834409}{7849475} y=\frac{117834409}{7849475} z=\frac{117834409}{7849475}$$