Let's denote the number of hamburgers sold as \( h \) and the number of hotdogs sold as \( d \).
From the problem, we have the following information:
- The total number of hamburgers and hotdogs sold is 300.
- The total revenue from hamburgers and hotdogs is $420.
We can set up the following system of equations based on this information:
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Total items sold: \[ h + d = 300 \]
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Total money made: \[ 2h + 1d = 420 \]
Now, let's match this system of equations with the given options:
- The first equation \( h + d = 300 \) represents the total items sold.
- The second equation \( 2h + d = 420 \) represents the total revenue made.
The correct system of equations matches the one we've formed:
\[ \begin{align*} h + d &= 300 \ 2h + d &= 420 \end{align*} \]
Looking at the options provided:
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Option A: \[ gh + d = 300 \ 12h + d = 420 \] This does not match.
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Option B: \[ Sh + d = 420 \ 12h + d = 300 \] This does not match.
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Option C: \[ jh + d = 300 \ n + 2d = 420 \] This does not match.
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Option D: \[ jh + d = 720 \ 12h + d = 300 \] This does not match.
None of the options provided exactly match the system of equations derived from the problem statement. The correct representation of the problem is:
\[ \begin{align*} h + d &= 300 \ 2h + d &= 420 \end{align*} \]
If jh corresponds to h, then choice C looks close but would need adjustments. Since no options are exactly correct, please verify provided options or explore additional details.