Question

The annual bonus given to the employees of a company is 5% of their taxable incomes, after the state and central taxes are deducted. The state tax is 10% of taxable income. The central tax is 20% of taxable income after deducting the state tax. Formulate this situation for determining the bonus, as a linear system.
Solve by substitution, the system you have obtained in

Answer 1

Answer on Question #75937 – Math – Algebra

Question

1. The annual bonus given to the employees of a company is 5% of their taxable incomes, after the state and central taxes are deducted. The state tax is 10% of taxable income. The central tax is 20% of taxable income after deducting the state tax. Formulate this situation for determining the bonus, as a linear system.

Solve by substitution, the system you have obtained in .

Solution

Let $x$ be amount of taxable incomes, $a$ be state tax, $b$ be central tax, $c$ be annual bonus, $B$ be amount of annual bonus.

Then

$$B = c \big ((x - a x) - b (x - a x) \big) = c \big ((1 - a) x - b (1 - a) x \big) = c (1 - b) (1 - a) x,$$

where

- $ax$ is amount of state tax

- $x - ax$ is taxable amount incomes after deducting the state tax

- $b(x - ax)$ is amount of central tax

After substitution $c = 0.05(5\%)$, $a = 0.1(10\%)$, $b = 0.2(20\%)$, one gets

$$B = 0.05(1 - 0.2)(1 - 0.1)x = 0.036x$$

Answer: 0.036x, where x is amount of taxable incomes.

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