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?

Question

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.