Solve {l}{m=0*25}{n=5*7}{o=1*6*{(1/8m+2*5n)}-{(4*5n-{(frac{1*{(2)}+1}{2})}m)}{(-2)}-{(-12m+14n)}}{text{Solvefor}ptext{where}}{p=o}

$$\left. \begin{array} { l } { m = 0 \cdot 25 }\\ { n = 5 \cdot 7 }\\ { o = 1 \cdot 6 \cdot {(\frac{1}{8} m + 2 \cdot 5 n)} - {(4 \cdot 5 n - {(\frac{1 \cdot {(2)} + 1}{2})} m)} {(-2)} - {(-12 m + 14 n)} }\\ { \text{Solve for } p \text{ where} } \\ { p = o } \end{array} \right.$$

Solve for m, n, o, p

$$p=3010$$

Solution Steps

Consider the first equation. Multiply 0 and 25 to get 0.

$$m=0$$

Consider the second equation. Multiply 5 and 7 to get 35.

$$n=35$$

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

$$o=1\times 6\left(\frac{1}{8}\times 0+2\times 5\times 35\right)-\left(4\times 5\times 35-\frac{1\times 2+1}{2}\times 0\right)\left(-2\right)-\left(-12\times 0+14\times 35\right)$$

Multiply 1 and 6 to get 6.

$$o=6\left(\frac{1}{8}\times 0+2\times 5\times 35\right)-\left(4\times 5\times 35-\frac{1\times 2+1}{2}\times 0\right)\left(-2\right)-\left(-12\times 0+14\times 35\right)$$

Multiply \frac{1}{8} and 0 to get 0.

$$o=6\left(0+2\times 5\times 35\right)-\left(4\times 5\times 35-\frac{1\times 2+1}{2}\times 0\right)\left(-2\right)-\left(-12\times 0+14\times 35\right)$$

Multiply 2 and 5 to get 10.

$$o=6\left(0+10\times 35\right)-\left(4\times 5\times 35-\frac{1\times 2+1}{2}\times 0\right)\left(-2\right)-\left(-12\times 0+14\times 35\right)$$

Multiply 10 and 35 to get 350.

$$o=6\left(0+350\right)-\left(4\times 5\times 35-\frac{1\times 2+1}{2}\times 0\right)\left(-2\right)-\left(-12\times 0+14\times 35\right)$$

Add 0 and 350 to get 350.

$$o=6\times 350-\left(4\times 5\times 35-\frac{1\times 2+1}{2}\times 0\right)\left(-2\right)-\left(-12\times 0+14\times 35\right)$$

Multiply 6 and 350 to get 2100.

$$o=2100-\left(4\times 5\times 35-\frac{1\times 2+1}{2}\times 0\right)\left(-2\right)-\left(-12\times 0+14\times 35\right)$$

Multiply 4 and 5 to get 20.

$$o=2100-\left(20\times 35-\frac{1\times 2+1}{2}\times 0\right)\left(-2\right)-\left(-12\times 0+14\times 35\right)$$

Multiply 20 and 35 to get 700.

$$o=2100-\left(700-\frac{1\times 2+1}{2}\times 0\right)\left(-2\right)-\left(-12\times 0+14\times 35\right)$$

Multiply 1 and 2 to get 2.

$$o=2100-\left(700-\frac{2+1}{2}\times 0\right)\left(-2\right)-\left(-12\times 0+14\times 35\right)$$

Add 2 and 1 to get 3.

$$o=2100-\left(700-\frac{3}{2}\times 0\right)\left(-2\right)-\left(-12\times 0+14\times 35\right)$$

Multiply \frac{3}{2} and 0 to get 0.

$$o=2100-\left(700-0\right)\left(-2\right)-\left(-12\times 0+14\times 35\right)$$

Subtract 0 from 700 to get 700.

$$o=2100-700\left(-2\right)-\left(-12\times 0+14\times 35\right)$$

Multiply 700 and -2 to get -1400.

$$o=2100-\left(-1400\right)-\left(-12\times 0+14\times 35\right)$$

The opposite of -1400 is 1400.

$$o=2100+1400-\left(-12\times 0+14\times 35\right)$$

Add 2100 and 1400 to get 3500.

$$o=3500-\left(-12\times 0+14\times 35\right)$$

Do the multiplications.

$$o=3500-\left(0+490\right)$$

Add 0 and 490 to get 490.

$$o=3500-490$$

Subtract 490 from 3500 to get 3010.

$$o=3010$$

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

$$p=3010$$

The system is now solved.

$$m=0 n=35 o=3010 p=3010$$