Solve {l}{y/2/3=6/24/25}{z=y}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { y / \frac{2}{3} = 6 / \frac{24}{25} }\\ { z = y }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for y, z, a

$$a = \frac{25}{6} = 4\frac{1}{6} \approx 4.166666667$$

Solution Steps

Consider the first equation. Divide 6 by \frac{24}{25} by multiplying 6 by the reciprocal of \frac{24}{25}.

$$\frac{y}{\frac{2}{3}}=6\times \frac{25}{24}$$

Multiply 6 and \frac{25}{24} to get \frac{25}{4}.

$$\frac{y}{\frac{2}{3}}=\frac{25}{4}$$

Multiply both sides by \frac{2}{3}.

$$y=\frac{25}{4}\times \frac{2}{3}$$

Multiply \frac{25}{4} and \frac{2}{3} to get \frac{25}{6}.

$$y=\frac{25}{6}$$

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

$$z=\frac{25}{6}$$

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

$$a=\frac{25}{6}$$

The system is now solved.

$$y=\frac{25}{6} z=\frac{25}{6} a=\frac{25}{6}$$