Problem Solving

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?

The answer choice is : 50 + (I/40).

Please help me to solve this problem.

Regards,

P.

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. ]

Consider this phrase,
[i][the average (arithmetic mean) of 100 units of country R's currency and 1 percent of one's annual income][/i]

(100 + (I/100))/2 = Avg arithmetic mean of 100 and 1% of I = 50 + (I/200)

Now, add 2% of one's annual income to this as follows: = (2I/100) + 50 +(I/200) = I/40 + 50 = OA

-Deepak

The only confusing part of this question is "average (arithmetic mean) of 100 units of country R's currency and 1 percent of one's annual income"
What it really means is much simpler: average of 100 and amount equal to 1% of Income, both of which have same units. 1% of income is I*1/100 which equals I/100. Average of I/100 and 100 is {100 + (I/100)}/2.
Now, {100 + (I/100)}/2 can be rewritten as 100/2 + (I/100)/2 = 50 +I/200
2% of I = 2I/100 = I/50
Now adding 2% of I + the average term,
I/50 + 50 + I/200 = 4I/200 + 50 + I/200 = 5I/200 + 50 = I/40 + 50