Question

Alejandro bought $3.50 worth of pencils and erasers at the school store. Pencils cost $0.50 apiece, and erasers cost $0.75 apiece. Which equation written in standard form represents the number of pencils, p, and the number of erasers, e, that Alejandro bought?

0.75e = 3.50 – 0.50p
0.50p + 0.75e = 3.50
3e = 14 – 2p
2p + 3e = 14

Answer 1

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.