Solve Q_{1}=600-4P_{A}-0.03M-12P_{A}+15G+6P_{B}+1.5N

$$Q _ { 1 } = 600 - 4 P _ { A } - 0.03 M - 12 P _ { A } + 15 G + 6 P _ { B } + 1.5 N$$

Solve for G

$$G=\frac{M}{500}+\frac{Q_{1}}{15}+\frac{16P_{A}}{15}-\frac{N}{10}-\frac{2P_{B}}{5}-40$$

Steps for Solving Linear Equation

Combine -4P_{A} and -12P_{A} to get -16P_{A}.

$$Q_{1}=600-16P_{A}-0.03M+15G+6P_{B}+1.5N$$

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

$$600-16P_{A}-0.03M+15G+6P_{B}+1.5N=Q_{1}$$

Subtract 600 from both sides.

$$-16P_{A}-0.03M+15G+6P_{B}+1.5N=Q_{1}-600$$

Add 16P_{A} to both sides.

$$-0.03M+15G+6P_{B}+1.5N=Q_{1}-600+16P_{A}$$

Add 0.03M to both sides.

$$15G+6P_{B}+1.5N=Q_{1}-600+16P_{A}+0.03M$$

Subtract 6P_{B} from both sides.

$$15G+1.5N=Q_{1}-600+16P_{A}+0.03M-6P_{B}$$

Subtract 1.5N from both sides.

$$15G=Q_{1}-600+16P_{A}+0.03M-6P_{B}-1.5N$$

The equation is in standard form.

$$15G=\frac{3M}{100}-\frac{3N}{2}+Q_{1}+16P_{A}-6P_{B}-600$$

Divide both sides by 15.

$$\frac{15G}{15}=\frac{\frac{3M}{100}-\frac{3N}{2}+Q_{1}+16P_{A}-6P_{B}-600}{15}$$

Dividing by 15 undoes the multiplication by 15.

$$G=\frac{\frac{3M}{100}-\frac{3N}{2}+Q_{1}+16P_{A}-6P_{B}-600}{15}$$

Divide Q_{1}-600+16P_{A}+\frac{3M}{100}-6P_{B}-\frac{3N}{2} by 15.

$$G=\frac{M}{500}+\frac{Q_{1}}{15}+\frac{16P_{A}}{15}-\frac{N}{10}-\frac{2P_{B}}{5}-40$$

Solve for M

$$M=-\frac{100Q_{1}}{3}-\frac{1600P_{A}}{3}+50N+200P_{B}+500G+20000$$

Steps for Solving Linear Equation

Combine -4P_{A} and -12P_{A} to get -16P_{A}.

$$Q_{1}=600-16P_{A}-0.03M+15G+6P_{B}+1.5N$$

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

$$600-16P_{A}-0.03M+15G+6P_{B}+1.5N=Q_{1}$$

Subtract 600 from both sides.

$$-16P_{A}-0.03M+15G+6P_{B}+1.5N=Q_{1}-600$$

Add 16P_{A} to both sides.

$$-0.03M+15G+6P_{B}+1.5N=Q_{1}-600+16P_{A}$$

Subtract 15G from both sides.

$$-0.03M+6P_{B}+1.5N=Q_{1}-600+16P_{A}-15G$$

Subtract 6P_{B} from both sides.

$$-0.03M+1.5N=Q_{1}-600+16P_{A}-15G-6P_{B}$$

Subtract 1.5N from both sides.

$$-0.03M=Q_{1}-600+16P_{A}-15G-6P_{B}-1.5N$$

The equation is in standard form.

$$-0.03M=-\frac{3N}{2}+Q_{1}+16P_{A}-6P_{B}-15G-600$$

Divide both sides of the equation by -0.03, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-0.03M}{-0.03}=\frac{-\frac{3N}{2}+Q_{1}+16P_{A}-6P_{B}-15G-600}{-0.03}$$

Dividing by -0.03 undoes the multiplication by -0.03.

$$M=\frac{-\frac{3N}{2}+Q_{1}+16P_{A}-6P_{B}-15G-600}{-0.03}$$

Divide Q_{1}-600+16P_{A}-15G-6P_{B}-\frac{3N}{2} by -0.03 by multiplying Q_{1}-600+16P_{A}-15G-6P_{B}-\frac{3N}{2} by the reciprocal of -0.03.

$$M=-\frac{100Q_{1}}{3}-\frac{1600P_{A}}{3}+50N+200P_{B}+500G+20000$$