500 PS

[dunkin77]

Hi,

for some reason, my answer was $12,300 which is not even on the choices. The answer is B) can anyone please explain?


After paying a 10 percent tax on all income over $3,000, a person had a net income of $12,000. What was the income before taxes?
(A) $13,300
(B) $13,000
(C) $12,900
(D) $10,000
(E) $9,000

[vk.neni]

The question is asking for the net income before taxes. The taxes are levied on income after the first 3000.

Assume income before taxes is x.

The total net income after taxes: (x-3000) * 0.9 + 3000 = 12000
(x-3000) * 0.9 = 9000
x = 9000/0.9 + 3000
x = 13000

0.9 above is the income left after taxes of 10%.

Answer is B

[dunkin77]

Oh - I got it! Thank you!

[BTGmoderatorRO]

let the initial income paying tax be x.
$$Now,\ 10\%\ of\ x=\frac{10}{100}\cdot x$$
After paying/removing 10% tax, we have ,
=x - 10% of x = 12000
i.e x-001x = 12000
0.9x = 12000
$$x=\frac{12000}{0.9}=\ $13333\ \frac{1}{3}$$
Therefore, the initial income before taxes is $13333 (1/3);
Thus, the closest answer from the available options is $13,300 which is option A

[Scott@TargetTestPrep]

Hi,

for some reason, my answer was $12,300 which is not even on the choices. The answer is B) can anyone please explain?


After paying a 10 percent tax on all income over $3,000, a person had a net income of $12,000. What was the income before taxes?
(A) $13,300
(B) $13,000
(C) $12,900
(D) $10,000
(E) $9,000

Let T = the income before taxes. Then (T - 3000) represents the part of the income that is taxable, and he gets to keep 90% of that amount after taxes are taken out. We can create the equation:

12,000 = 3,000 + 0.9(T - 3000)

9,000 = 0.9T - 2,700

11,700 = 0.9T

13,000 = T

Answer: B