in certain country families with anet incame of over 18000 birr must pey an incame tax of 3000 birr plus 30% of the amount over 18000 birr what is the range of the net income of families who pay an income tax between 3483 birr &4050 birr?
Let i be the income, and t be the amount of taxes
t = 3000 + .3(i - 1800)
if t = 3483, then 3483 = 3000 + .3(i - 1800)
.3(i - 1800) = 483
i - 1800 = 1610
i = 3410 <------ income for lower tax paid.
if t = 4050 .......
do the second income the same way, and you got your range.
Boba
To find the range of net income for families who pay an income tax between 3483 birr and 4050 birr, we need to reverse the income tax calculation and determine the range of net income that would result in these tax amounts.
Let's start by calculating the income tax for each end of the range:
For the lower end of the range (3483 birr), we can set up the following equation:
3483 = 3000 + 0.3 * (net income - 18000)
Simplifying the equation:
3483 - 3000 = 0.3 * (net income - 18000)
483 = 0.3 * (net income - 18000)
Dividing by 0.3:
483 / 0.3 = net income - 18000
1610 = net income - 18000
Adding 18000 to both sides:
1610 + 18000 = net income
19610 = net income
So, for a net income of 3483 birr, the gross income should be 19610 birr.
Now, for the upper end of the range (4050 birr), we can set up a similar equation:
4050 = 3000 + 0.3 * (net income - 18000)
Simplifying the equation:
4050 - 3000 = 0.3 * (net income - 18000)
1050 = 0.3 * (net income - 18000)
Dividing by 0.3:
1050 / 0.3 = net income - 18000
3500 = net income - 18000
Adding 18000 to both sides:
3500 + 18000 = net income
21500 = net income
So, for a net income of 4050 birr, the gross income should be 21500 birr.
Therefore, the range of net income for families who pay an income tax between 3483 birr and 4050 birr is 19610 birr to 21500 birr.