Solve {l}{0.5/0.15=n/1.2}{o=n}{p=o}{q=p}{r=q}{s=r}{t=s}{u=t}{v=u}{w=v}{x=w}{y=x}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { \frac{0.5}{0.15} = \frac{n}{1.2} }\\ { o = n }\\ { p = o }\\ { q = p }\\ { r = q }\\ { s = r }\\ { t = s }\\ { u = t }\\ { v = u }\\ { w = v }\\ { x = w }\\ { y = x }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for n, o, p, q, r, s, t, u, v, w, x, y, z

$$z=4$$

Solution Steps

Consider the first equation. Expand \frac{0.5}{0.15} by multiplying both numerator and the denominator by 100.

$$\frac{50}{15}=\frac{n}{1.2}$$

Reduce the fraction \frac{50}{15} to lowest terms by extracting and canceling out 5.

$$\frac{10}{3}=\frac{n}{1.2}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{n}{1.2}=\frac{10}{3}$$

Multiply both sides by 1.2.

$$n=\frac{10}{3}\times 1.2$$

Multiply \frac{10}{3} and 1.2 to get 4.

$$n=4$$

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

$$o=4$$

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

$$p=4$$

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

$$q=4$$

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

$$r=4$$

Consider the equation (6). Insert the known values of variables into the equation.

$$s=4$$

Consider the equation (7). Insert the known values of variables into the equation.

$$t=4$$

Consider the equation (8). Insert the known values of variables into the equation.

$$u=4$$

Consider the equation (9). Insert the known values of variables into the equation.

$$v=4$$

Consider the equation (10). Insert the known values of variables into the equation.

$$w=4$$

Consider the equation (11). Insert the known values of variables into the equation.

$$x=4$$

Consider the equation (12). Insert the known values of variables into the equation.

$$y=4$$

Consider the equation (13). Insert the known values of variables into the equation.

$$z=4$$

The system is now solved.

$$n=4 o=4 p=4 q=4 r=4 s=4 t=4 u=4 v=4 w=4 x=4 y=4 z=4$$