Question

b what is the price after gst has been added?
22 an advertisement states save 15%. we pay the gst! investigate this statement.

Explanation:

Analyze the advertisement statement

We need to investigate the claim: "Save 15%. We pay the GST".
Let the original price of the item before any discount and before GST be \(P\).
In Australia/New Zealand, the standard Goods and Services Tax (GST) is \(10\%\).
Using the GST Calculation knowledge point, the price including GST is:

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

Calculate the discounted price

Using the Percentage Discount Analysis knowledge point, a \(15\%\) discount on the original price \(P\) yields:

$$ P_{\text{discount}} = P \times (1 - 0.15) = P \times 0.85 $$

Compare the two scenarios

If the store "pays the GST" on the discounted price, the customer pays the discounted price \(P \times 0.85\), which already includes the GST.
This means the pre-GST price of the discounted item is:

$$ P_{\text{pre-GST, discounted}} = \frac{P \times 0.85}{1.10} \approx P \times 0.7727 $$

The total savings for the customer compared to the standard retail price (which is \(P \times 1.10\)) is:

$$ \text{Actual Savings} = \frac{(P \times 1.10) - (P \times 0.85)}{P \times 1.10} = \frac{0.25}{1.10} \approx 22.73\% $$

Evaluate the claim

If the advertisement means the customer saves \(15\%\) off the GST-inclusive price, and the store pays the \(10\%\) GST out of that, the customer pays:

$$ P_{\text{final}} = (P \times 1.10) \times 0.85 = P \times 0.935 $$

In this case, the actual discount is exactly \(15\%\). The store "paying the GST" simply means the GST is calculated from this final paid amount:

$$ \text{GST Paid by Store} = \frac{P \times 0.935}{11} = P \times 0.085 $$

Both interpretations show that the customer receives a genuine discount, and the store still accounts for the required GST within the final transaction price.

Answer:

To investigate the statement "Save 15%. We pay the GST":

1. Interpretation 1 (Discount on GST-inclusive price):

If a \(15\%\) discount is applied to the standard retail price (which already includes \(10\%\) GST):

$$ \text{Price Paid} = \text{Retail Price} \times 0.85 $$

The store "pays the GST" by extracting the \(10\%\) GST component from this final amount paid by the customer:

$$ \text{GST Component} = \frac{\text{Price Paid}}{11} $$

In this scenario, the customer saves exactly \(15\%\).

1. Interpretation 2 (Saving 15% and not paying the 10% GST):

If the customer saves \(15\%\) on the pre-GST price and does not pay the \(10\%\) GST:

$$ \text{Price Paid} = \text{Pre-GST Price} \times 0.85 $$

Compared to the normal retail price (\(\text{Pre-GST Price} \times 1.10\)), the actual saving is:

$$ \text{Actual Savings} = \frac{1.10 - 0.85}{1.10} \approx 22.73\% $$

In both cases, the statement is a marketing strategy where the store reduces its profit margin to cover the tax obligation while offering a discount to the customer.