Solve a(800-80)+(8a-a)(1200-280)=30000

$$a ( 800 - 80 ) + ( 8 a - a ) ( 1200 - 280 ) = 30000$$

Solve for a

$$a = \frac{750}{179} = 4\frac{34}{179} \approx 4.189944134$$

Steps for Solving Linear Equation

Subtract 80 from 800 to get 720.

$$a\times 720+\left(8a-a\right)\left(1200-280\right)=30000$$

Combine 8a and -a to get 7a.

$$a\times 720+7a\left(1200-280\right)=30000$$

Subtract 280 from 1200 to get 920.

$$a\times 720+7a\times 920=30000$$

Multiply 7 and 920 to get 6440.

$$a\times 720+6440a=30000$$

Combine a\times 720 and 6440a to get 7160a.

$$7160a=30000$$

Divide both sides by 7160.

$$a=\frac{30000}{7160}$$

Reduce the fraction \frac{30000}{7160} to lowest terms by extracting and canceling out 40.

$$a=\frac{750}{179}$$