As a result of several mergers and acquisitions, stock

in four companies has been distributed among the

companies. Each row of the following table gives the

percentage of stock in the four companies that a

particular company owns and the annual net income

of each company.

So company A holds $80\%$ of its own stock, $11\%$ of the

stock in company B$,4\%$ of the stock in company C$,$

etc. For the purpose of assessing a state tax on

corporate income, the taxable income of each

company is defined to be its share of its own annual

net income plus its share of the taxable income of

each of the other companies, as determined by the

percentages in the table. What is the taxable income

of each company $($to the nearest thousand dollars$)?$

Use the variables $x_1$ to represent taxable

income of company $A,x_2$ to represent taxable

income of company $B,x_3$ to represent taxable

income of company $C,$ and $x_4$ to represent

taxable income of company $D,$ and write the

system of equations that can be used to find

all of the taxable incomes in millions of dollars.

The equation that represents the calculation of

company A$\text{'}$s taxable income is

$x_1-0\mathrm{.}11x_2-0\mathrm{.}04x_3-0\mathrm{.}1x_4=2\mathrm{.}56.$

The equation that represents the calculation of

company B$\text{'}$s taxable income is

$-0\mathrm{.}13x_1+x_2-0\mathrm{.}11x_3-0\mathrm{.}14x_4=2\mathrm{.}184.$

The equation that represents the calculation of

company C$\text{'}$s taxable income is

$-0\mathrm{.}05x_1-0\mathrm{.}08x_2+x_3-0\mathrm{.}1x_4={3\mathrm{.}276}^{\text{'}}.$

The equation that represents the calculation of

company D$\text{'}$s taxable income is

$-0\mathrm{.}02x_1-0\mathrm{.}03x_2-0\mathrm{.}07x_3+x_4=2\mathrm{.}244\text{'}.$

$($Simplify your answers. Use integers or

decimals for any numbers in the equations.$)$

The taxable income for company A is $

million. The taxable income for company $B$ is

$ million. The taxable income for company

$C$ is $ million. The taxable income for

company $D$ is $ million.

$($Round to the nearest thousandth as needed.$)$