To calculate the price of a necklace without GST, we need to understand the relationship between the price with GST and the GST percentage.
Given:
- Final price with GST included = [tex]$63
- GST percentage = 15%
To find the price without GST, we'll denote:
- Price without GST as \( P \)
The relationship between the final price and the price without GST including the GST percentage can be expressed as:
\[
\text{Price with GST} = \text{Price without GST} \times (1 + \frac{\text{GST percentage}}{100})
\]
Substituting the known values:
\[
63 = P \times (1 + \frac{15}{100})
\]
\[
63 = P \times 1.15
\]
To isolate \( P \), we divide both sides of the equation by 1.15:
\[
P = \frac{63}{1.15}
\]
When we carry out this division:
\[
P \approx 54.78260869565218
\]
Thus, the price of the necklace without GST is approximately \$[/tex]54.78.
Therefore, the exact and detailed step-by-step solution concludes that the price without including the GST, correctly calculated, is \$54.78.
