Question

below shows pauls business cell phone charges for one month.
(a) the bill shows a total amount due of $158.88,
this includes charges of $38.88.
what percentage of the total amount are the charges?
(b) the previous months charge was $207.86 incl gst.
what is the gst exclusive price of last months charges?
(c) the current total charge is $158.88. the previous total charge was $207.86.
calculate the percentage change in pauls cell phone charge from the previous months charge.
(d) the cell phone pricing plan is broken up into a talk charge and a data charge in the ratio of 2:5.
from the pricing plan charge of $104.35, calculate the amount of the data charge.

Explanation:

Step1: Calculate percentage for (a)

Percentage formula: $\frac{\text{Part}}{\text{Whole}}\times100$. Here, part is $38.88$ and whole is $158.88$.
$\frac{38.88}{158.88}\times100=\frac{3888}{158.88}\approx24.47\%$

Step2: Find GST - exclusive price for (b)

Let the GST - exclusive price be $x$. If $x(1 + 0.1)=207.86$ (since GST is $10\%$ or $0.1$), then $x=\frac{207.86}{1.1}=188.96$

Step3: Calculate percentage change for (c)

Previous charge $=207.86$, New charge $=158.88$. Percentage change formula: $\frac{\text{New}-\text{Old}}{\text{Old}}\times100$.
$\frac{158.88 - 207.86}{207.86}\times100=\frac{- 48.98}{207.86}\times100\approx - 23.56\%$ (a decrease of approximately $23.56\%$)

Step4: Calculate ratio for (d)

Talk charge $=207.86-158.88 = 48.98$, Data charge $=158.88$. Ratio of talk charge to data charge: $\frac{48.98}{158.88}=\frac{4898}{15888}=\frac{2449}{7944}\approx0.308$ or as a ratio $48.98:158.88 = 2449:7944\approx30.8:100$

Answer:

(a) Approximately $24.47\%$; (b) $\$188.96$; (c) Approximately $- 23.56\%$ (a $23.56\%$ decrease); (d) Approximately $30.8:100$