Solve {l}{1000*60=frac{r_{w}}{150}}{text{cavity,}r_{w}=135.5m}

$$\left. \begin{array} { l } { 1000 \times 60 = \frac { r _ { w } } { 150 } } \\ { \text { cavity, } r _ { w } = 135.5 m } \end{array} \right.$$

Solve for r_w, m

$$r_{w}=9000000$$

$$m = \frac{18000000}{271} = 66420\frac{180}{271} \approx 66420.664206642$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 150.

$$150000\times 60=r_{w}$$

Multiply 150000 and 60 to get 9000000.

$$9000000=r_{w}$$

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

$$r_{w}=9000000$$

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

$$9000000=135.5m$$

Divide both sides by 135.5.

$$\frac{9000000}{135.5}=m$$

Expand \frac{9000000}{135.5} by multiplying both numerator and the denominator by 10.

$$\frac{90000000}{1355}=m$$

Reduce the fraction \frac{90000000}{1355} to lowest terms by extracting and canceling out 5.

$$\frac{18000000}{271}=m$$

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

$$m=\frac{18000000}{271}$$

The system is now solved.

$$r_{w}=9000000 m=\frac{18000000}{271}$$