The table shows personal income tax rates for different taxable incomes for a particular country.
A person with a taxable income of $88 000 pays 25.8% of that income in tax (excluding any levies). What is the value of `X` in the table? (3 marks)
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 52 cents for each $1 over $108 400
`text{Tax paid}\ =88\ 000 xx 0.258 = $22\ 704` `text{Equating with tax payable formula in the table:}`
`22\ 704`
`=18\ 292+X(88\ 000-78\ 800)`
`X(9\ 200)`
`=22\ 704-18\ 292`
`X`
`=4412 / 9200`
`=0.48\ text{dollars}`
`=48\ text{cents}`