The table below shows part of Ahmad's personal income tax bill.

1. Find the assessable income after subtracting approved donations from total income.

$p=123419.00-1543.00=121876.00$

2. Find the total personal reliefs by using assessable income and chargeable income.

Since
$\text{Chargeable Income}=\text{Assessable Income}-\text{Total Personal Reliefs},$
$q=121876.00-100058.00=21818.00$

1. Identify the relevant tax bracket and the taxable amount in that bracket.

Ahmad's chargeable income is $\char36{}100058.00$.

From the table, tax on the first $\char36{}80000$ is $\char36{}3350$.

Amount taxed at $11.5\%$:
$100058-80000=20058$

2. Calculate the tax on the remaining amount and add it to the tax on the first $80000$.

Tax on the next $\char36{}20058$:
$11.5\%\times 20058=0.115\times 20058=2306.67$

Total tax payable:
$3350+2306.67=5656.67$

1. Find Angie's income tax payable from Ahmad's income tax payable.

Ahmad's income tax payable is $\char36{}5656.67$.

Angie's income tax payable
$=0.55\times 5656.67=3111.1685\approx \$3111.17$

2. Identify the tax bracket for Angie's tax payable.

From the tax table:

Tax on the first $\char36{}40000$ is $\char36{}550$.

Tax on the first $\char36{}80000$ is $\char36{}3350$.

Since
$550<3111.17<3350,$
Angie's chargeable income is between $\char36{}40000$ and $\char36{}80000$.

So the extra income above $\char36{}40000$ is taxed at $7\%$.

3. Calculate Angie's actual chargeable income from her tax payable.

Extra tax above the first $\char36{}40000$:
$3111.17-550=2561.17$

Let the extra chargeable income above $\char36{}40000$ be $x$.

$7\%\text{ of }x=2561.17$
$0.07x=2561.17$
$x=\frac{2561.17}{0.07}=36588.142\ldots$

Angie's chargeable income
$=40000+36588.142\ldots=76588.142\ldots$
$\approx \$76588.14$

4. Compare Angie's actual chargeable income with 0.55 of Ahmad's chargeable income and conclude.

Ahmad's chargeable income is $\char36{}100058$.

$0.55$ of Ahmad's chargeable income
$=0.55\times 100058=55031.90$

But
$76588.14\ne 55031.90.$

Therefore, Angie's chargeable income is not $0.55$ of Ahmad's chargeable income.