Marcel purchased a television at a price that was less than its lis
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03 Aug 2025, 09:36
Let's start by defining the variables and information from the problem:
- Let the purchase price be $x$ dollars.
- The sales tax is 7.20 dollars.
- The sales tax rate (percentage) is $p \%$ of the purchase price.
By definition:
$$
\(\text { Sales tax }=\frac{p}{100} \times x=7.20\)
$$
Thus:
$$
\(p=\frac{7.20 \times 100}{x}=\frac{720}{x}\)
$$
To find $p$, we need to know $x$, the purchase price.
Now, let's analyze each additional statement to see if it provides enough information to uniquely determine $p$ :
AA: The total amount Marcel paid was 127.20.
This total includes purchase price plus sales tax:
$$
\(x+7.20=127.20 \Longrightarrow x=127.20-7.20=120.00\)
$$
Knowing $\(x=120\)$, compute $p$ :
$$
\(p=\frac{720}{120}=6\)
$$
A alone is sufficient to determine $p$.
B: The purchase price was 40.00 less than the list price.
This tells us:
$$
\(x=L-40\)
$$
where $L$ is the list price, unknown.
We only know $x$ is 40 less than $L$, but neither $x$ nor $L$ is given. The sales tax calculation depends on $x$, so without actual values, $p$ cannot be determined.
B alone is not sufficient.
C: The purchase price was $\(25 \)%$ less than the list price.
This means:
$$
\(x=L \times(1-0.25)=0.75 L\)
$$
Again, we do not know $L$ or $x$, so $p$ cannot be determined uniquely from this. C alone is not sufficient.
Final conclusion:
- A alone provides $x$, allowing calculation of $p$.
- $\(\mathbf{B }\)$ and $\(\mathbf{C }\)$ give relations involving the unknown list price $L$, but without any absolute values, $p$ cannot be determined.
Answer: Only A individually provides sufficient information to find $p$.