To formulate the correct equation that represents the situation described, we need to express the total cost of the pencils and erasers purchased by Alejandro.
Given:
- Each pencil costs $0.50
- Each eraser costs $0.75
- The total cost spent by Alejandro is $3.50
We can represent the total cost with the equation:
\[ \text{cost of pencils} + \text{cost of erasers} = \text{total cost} \]
This can be expressed as:
\[ 0.50p + 0.75e = 3.50 \]
This corresponds to the second equation listed in your options.
Now we can also manipulate this equation into standard form (which is generally written as \(Ax + By = C\) where A, B, and C are integers). To eliminate the decimals, we can multiply the entire equation by 100:
\[ 100(0.50p) + 100(0.75e) = 100(3.50) \]
This results in:
\[ 50p + 75e = 350 \]
Dividing through by 25 gives:
\[ 2p + 3e = 14 \]
Thus, the equation in standard form is:
Answer: \(2p + 3e = 14\)
Therefore, both \(0.50p + 0.75e = 3.50\) and \(2p + 3e = 14\) correctly represent the scenario depending on whether you prefer it in decimal form or standard integer form.
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