Question
Maria is organizing a charity bake sale. She has already spent $20 on baking supplies and plans to sell each batch of cookies for $15. Let x represent the number of batches of cookies Maria sells, and let y represent the total amount of money she makes from selling the cookies Which of the following linear equations represents the total amount of money Maria makes from selling x batches of cookies? (3 points) x = 15u + 20; y = 15x - 20; x = 20y + 15; y = 20x + 15
Answers
GPT-4o mini
To determine the correct linear equation for the total amount of money Maria makes from selling \( x \) batches of cookies, we first need to understand how to express her earnings based on the given information:
1. Maria sells each batch of cookies for $15.
2. She has already spent $20 on supplies.
The total revenue \( y \) from selling \( x \) batches of cookies can be represented as:
\[
y = 15x
\]
However, since she has already spent $20 on supplies, in order to determine profit (not just revenue), we subtract that from her total:
\[
\text{Profit} = \text{Revenue} - \text{Costs} = y - 20
\]
Thus, we derive the equation:
\[
y - 20 = 15x
\]
Rearranging that gives:
\[
y = 15x + 20
\]
None of the answer choices exactly match this equation. However, according to the context of the question and the possible intentions behind the equations, we need to understand that the only equation that would be aligning with growing \( y \) in relation to \( x \) while incorporating the adjustments related to costs would hint at that costs are taken out of the total \( y \).
Thus, while none of the answer options directly represent the intended profit scenario with costs taken into account correctly, the form we can deduce from your options would not reflect a proper setup.
Yet focusing explicitly on revenue without costs directly provides:
The one closest as a negative impact of costs would indeed relate typically in terms of sales, reflected in the market structure by the following entry:
\( y = 15x - 20 \)
This uses the profit stance if we were expressing how direct profits then are portrayed against against initial costs alone, hence this appears to likely be the choice. In a standard format for understanding profit margins and gross along with just revenue it may serve as industry best practice, whereas if costs are ignored it outlines as variances along the lines of pure revenue establishment alone.
So, the best linear equation that reflects revenue minus costs in that context is:
**Answer: \( y = 15x - 20 \)**
1. Maria sells each batch of cookies for $15.
2. She has already spent $20 on supplies.
The total revenue \( y \) from selling \( x \) batches of cookies can be represented as:
\[
y = 15x
\]
However, since she has already spent $20 on supplies, in order to determine profit (not just revenue), we subtract that from her total:
\[
\text{Profit} = \text{Revenue} - \text{Costs} = y - 20
\]
Thus, we derive the equation:
\[
y - 20 = 15x
\]
Rearranging that gives:
\[
y = 15x + 20
\]
None of the answer choices exactly match this equation. However, according to the context of the question and the possible intentions behind the equations, we need to understand that the only equation that would be aligning with growing \( y \) in relation to \( x \) while incorporating the adjustments related to costs would hint at that costs are taken out of the total \( y \).
Thus, while none of the answer options directly represent the intended profit scenario with costs taken into account correctly, the form we can deduce from your options would not reflect a proper setup.
Yet focusing explicitly on revenue without costs directly provides:
The one closest as a negative impact of costs would indeed relate typically in terms of sales, reflected in the market structure by the following entry:
\( y = 15x - 20 \)
This uses the profit stance if we were expressing how direct profits then are portrayed against against initial costs alone, hence this appears to likely be the choice. In a standard format for understanding profit margins and gross along with just revenue it may serve as industry best practice, whereas if costs are ignored it outlines as variances along the lines of pure revenue establishment alone.
So, the best linear equation that reflects revenue minus costs in that context is:
**Answer: \( y = 15x - 20 \)**