Solve {l}{2/9=N/3}{a=sqrt{144*225}}{b=a}{c=b}{text{Solvefor}dtext{where}}{d=c}

$$\left. \begin{array} { l } { \frac{2}{9} = \frac{N}{3} }\\ { a = \sqrt{144 \cdot 225} }\\ { b = a }\\ { c = b }\\ { \text{Solve for } d \text{ where} } \\ { d = c } \end{array} \right.$$

Solve for N, a, b, c, d

$$d=180$$

Solution Steps

Consider the first equation. Multiply both sides by 3.

$$\frac{2}{9}\times 3=N$$

Multiply \frac{2}{9} and 3 to get \frac{2}{3}.

$$\frac{2}{3}=N$$

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

$$N=\frac{2}{3}$$

Consider the second equation. Multiply 144 and 225 to get 32400.

$$a=\sqrt{32400}$$

Calculate the square root of 32400 and get 180.

$$a=180$$

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

$$b=180$$

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

$$c=180$$

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

$$d=180$$

The system is now solved.

$$N=\frac{2}{3} a=180 b=180 c=180 d=180$$