Solve a(800-b0)+(8a-a)(1200-280)=3000

$$a ( 800 - b 0 ) + ( 8 a - a ) ( 1200 - 280 ) = 3000$$

Solve for a

$$a=\frac{3000}{7240-b_{0}}$$

$$b_{0}\neq 7240$$

Steps for Solving Linear Equation

Use the distributive property to multiply a by 800-b_{0}.

$$800a-ab_{0}+\left(8a-a\right)\left(1200-280\right)=3000$$

Combine 8a and -a to get 7a.

$$800a-ab_{0}+7a\left(1200-280\right)=3000$$

Subtract 280 from 1200 to get 920.

$$800a-ab_{0}+7a\times 920=3000$$

Multiply 7 and 920 to get 6440.

$$800a-ab_{0}+6440a=3000$$

Combine 800a and 6440a to get 7240a.

$$7240a-ab_{0}=3000$$

Combine all terms containing a.

$$\left(7240-b_{0}\right)a=3000$$

Divide both sides by 7240-b_{0}.

$$\frac{\left(7240-b_{0}\right)a}{7240-b_{0}}=\frac{3000}{7240-b_{0}}$$

Dividing by 7240-b_{0} undoes the multiplication by 7240-b_{0}.

$$a=\frac{3000}{7240-b_{0}}$$

Solve for b_0

$$b_{0}=7240-\frac{3000}{a}$$

$$a\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply a by 800-b_{0}.

$$800a-ab_{0}+\left(8a-a\right)\left(1200-280\right)=3000$$

Combine 8a and -a to get 7a.

$$800a-ab_{0}+7a\left(1200-280\right)=3000$$

Subtract 280 from 1200 to get 920.

$$800a-ab_{0}+7a\times 920=3000$$

Multiply 7 and 920 to get 6440.

$$800a-ab_{0}+6440a=3000$$

Combine 800a and 6440a to get 7240a.

$$7240a-ab_{0}=3000$$

Subtract 7240a from both sides.

$$-ab_{0}=3000-7240a$$

The equation is in standard form.

$$\left(-a\right)b_{0}=3000-7240a$$

Divide both sides by -a.

$$\frac{\left(-a\right)b_{0}}{-a}=\frac{3000-7240a}{-a}$$

Dividing by -a undoes the multiplication by -a.

$$b_{0}=\frac{3000-7240a}{-a}$$

Divide 3000-7240a by -a.

$$b_{0}=7240-\frac{3000}{a}$$