Question

Mary's salary is $X per annum. The tax system is such that Mary pays a 15% flat rate of income tax on her salary. The tax system is due for reform, and politicians have suggested the following: Any income under $7,500 should be tax free. Any income above $7,500 should be taxed at 25% on the amount over $7,500. Given that Mary will be paying exactly the same amount of tax under both systems, calculate the amount of tax that Mary pays.

Answer 1

Answer:

The real answer is 18750

Step-by-step explanation:

Answer 2

Answer:

The of tax is $ 2812.50

Step-by-step explanation:

Given that Mary's salary is $x per year, then applying the 15% flat tax rate will give the amount paid for tax as;

15/100 *x =0.15 x -----equation (i)

After reforms , Mary still pays a tax similar to the original system. This means the amount of Mary's salary is above $7500.

Mary's amount above is the flat rate of $7500 is ;

$(x-7500)

Applying the 25% tax will give;

25/100 ( x-7500)

0.25(x-7500)

0.25x -1875 --------equation (ii)

Equating the two equations

0.15x = 0.25x - 1875

collect like terms

1875=0.25x-0.15

1875 =0.10x

Divide both sides by 0.10 to get x

1875/0.10 = 0.10x/0.10

18750 = x

The amount of Mary's salary is $18750

The amount of tax she pays is;

0.15 * 18750 =$ 2812.50