Solve 3a+400b=2.4a+600b

$$3 a + 400 b = 2.4 a + 600 b$$

Solve for a

$$a=\frac{1000b}{3}$$

Steps for Solving Linear Equation

Subtract 2.4a from both sides.

$$3a+400b-2.4a=600b$$

Combine 3a and -2.4a to get 0.6a.

$$0.6a+400b=600b$$

Subtract 400b from both sides.

$$0.6a=600b-400b$$

Combine 600b and -400b to get 200b.

$$0.6a=200b$$

Divide both sides of the equation by 0.6, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{0.6a}{0.6}=\frac{200b}{0.6}$$

Dividing by 0.6 undoes the multiplication by 0.6.

$$a=\frac{200b}{0.6}$$

Divide 200b by 0.6 by multiplying 200b by the reciprocal of 0.6.

$$a=\frac{1000b}{3}$$

Solve for b

$$b=\frac{3a}{1000}$$

Steps for Solving Linear Equation

Subtract 600b from both sides.

$$3a+400b-600b=2.4a$$

Combine 400b and -600b to get -200b.

$$3a-200b=2.4a$$

Subtract 3a from both sides.

$$-200b=2.4a-3a$$

Combine 2.4a and -3a to get -0.6a.

$$-200b=-0.6a$$

The equation is in standard form.

$$-200b=-\frac{3a}{5}$$

Divide both sides by -200.

$$\frac{-200b}{-200}=-\frac{\frac{3a}{5}}{-200}$$

Dividing by -200 undoes the multiplication by -200.

$$b=-\frac{\frac{3a}{5}}{-200}$$

Divide -\frac{3a}{5} by -200.

$$b=\frac{3a}{1000}$$