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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.

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ciarasworld314

Answer:

2812.50

Step-by-step explanation:

To find X we calculate how much tax is paid under both systems (in terms of X) and equate them, so

15%×X=25%×(X−7,500),

that is  

0.15X=0.25X−1,875⟹0.1X=1,875,

which solves to give X=$18,750. We can use either system to calculate the amount of tax Mary pays, but the first is easier. Therefore we have

Tax Payable (Current System)=$18,750×15%=$2,812.50.

Incidentally, let's just check that the new system agrees. We have

Tax Payable (Proposed System)=$(18,750−7,500)×25%=$2,812.50.

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