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2 years ago

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Before being simplified, the instructions for computing income tax in Country R were to add 2 percent of one’s annual income to

the average (arithmetic mean) of 100 units of Country R’s currency and 1 percent of one’s annual income. Which of the following represents the simplified formula for computing the income tax, in Country R’s currency, for a person in that country whose annual income is I ?
A. 50 + I/200
B. 50 + 3I/100
C. 50 + I/40
D. 100 + I/50
E. 100 + 3I/100

1 answer:

Vedmedyk [2.9K]2 years ago

6 0

Answer:

Option C)

$50 + \dfrac{I}{40}$

Step-by-step explanation:

We are given the following in the question:

I is the annual income of a person in a country R

2 percent of one’s annual income =

$\dfrac{2}{100}\times I = 0.02I$

1 percent of one’s annual income =

$\dfrac{1}{100}\times I = 0.01I$

Average of 100 units of Country R’s currency and 1 percent of one’s annual income.

$=\dfrac{0.01I + 100}{2}$

Income tax =

2 percent of one’s annual income + Average of 100 units of Country R’s currency and 1 percent of one’s annual income.

$= 0.02I + \dfrac{100+0.01I}{2}\\\\=50 + \dfrac{0.04I + 0.01I}{2}\\\\=50 + \dfrac{0.05I}{2}\\\\= 50 + \dfrac{I}{40}$

Thus, income tax is given by

Option C)

$50 + \dfrac{I}{40}$

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It's a method to optimize (maximize or minimize) functions of more than one variable subject to equality restrictions.

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