The table shows personal income tax rates for different taxable incomes for a particular country. Taxable income Tax payable $0 – $11 000 Nil $11 001 – $42 400 20 cents for each $1 over $11 000 $42 401 – $78 800 $6280 plus 33 cents for each $1 over $42 400 $78 801 – $108 400 $18 292 plus X cents for each $1 over $78 800 $108 401 and over $31 316 plus 48 cents for each $1 over $108 400 A person with a taxable income of $90 000 pays 25.8% of that income in tax (excluding any levies). What is the value of X in the table?

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The table shows personal income tax rates for different taxable incomes for a particular country - HSC - SSCE Mathematics Standard - Question 37 - 2023 - Paper 1

Question 37

The table shows personal income tax rates for different taxable incomes for a particular country. Taxable income Tax payable $0 – $11 000 Nil $11 001 – $42 400 20... show full transcript

Worked Solution & Example Answer:The table shows personal income tax rates for different taxable incomes for a particular country - HSC - SSCE Mathematics Standard - Question 37 - 2023 - Paper 1

Step 1

Calculate 25.8% of $90,000

96%

114 rated

Answer

$90,000 imes 0.258 =$ 23,220

Step 2

Calculate amount over $78,800

99%

104 rated

Answer

$90,000 -$ 78,800 = $11,200

Step 3

Calculate additional tax for amount over $78,800

96%

101 rated

Answer

Total tax paid for amount over $78,800 =$ 23,220 - $18,292 =$ 4,928

Step 4

Find the value of X

98%

120 rated

Answer

$11,200 imes X =$ 4,928

X = \frac{4,928}{11,200} \approx 0.440

X = 44\text{ cents}

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