Question

21 a scooter has gst of $42 added to its price.
a what is the value of the scooter before gst?
b what is the price after gst has been added?
22 an advertisement states save 15%. we pay the gst! investigate this statement.

Explanation:

Calculate the price of the scooter before GST

Using the GST Calculation and Tax Exclusive Pricing knowledge points

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Calculate the price of the scooter after GST

Using the Tax Inclusive Pricing knowledge point

$$
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Investigate the advertisement statement

We need to analyze the claim: "Save 15%. We pay the GST".
Let the original price before GST be \(P\).
The price with GST added is:

$$ P_{\text{with GST}} = 1.10P $$

If the store "pays the GST", the customer pays the price without GST, which is \(P\).
The actual savings for the customer is:

$$ \text{Savings} = P_{\text{with GST}} - P = 0.10P $$

We calculate the percentage savings relative to the total price with GST:

$$ \text{Percentage Savings} = \frac{0.10P}{1.10P} \approx 9.09\% $$

Since \(9.09\% < 15\%\), the statement "Save 15%" is mathematically incorrect and misleading.

Answer:

Question 21a

The value of the scooter before GST is $420.

Question 21b

The price after GST has been added is $462.

Question 22

The statement is mathematically incorrect.

If a business "pays the GST" (which is \(10\%\)), they are selling the item at its pre-GST price. The savings relative to the GST-inclusive price is:

$$ \frac{10\%}{110\%} \approx 9.09\% $$

This is significantly less than the advertised \(15\%\) savings.