Otto has some whipping cream that is

Question

Otto has some whipping cream that is

\[30\%\] butterfat and some milk that is
\[2\%\] butterfat. He wants to make a
\[500\,\text{mL}\] mixture of them that is
\[12\%\] butterfat.
Here's a graph that shows a system of equations for this scenario where
\[x\] is the volume of whipping cream he uses and
\[y\] is the volume of milk he uses.
A graph with two lines and a point. Line A is labeled 0.30 times x plus 0.02 times y equals 0.12 times 500. Line B is labeled x plus y equals 500. Point J is on line A and above line B.
\[\small{200}\]
\[\small{400}\]
\[\small{600}\]
\[\small{200}\]
\[\small{400}\]
\[\small{600}\]
\[\small{800}\]
\[\small{1000}\]
\[y\,\text{(milk)}\]
\[x\,\text{(cream)}\]
\[\text{line }b: x+y=500\]
\[\text{line }a: 0.30x+0.02y=0.12(500)\]
\[J\]
What does point
\[J\] represent in this context?
Choose 1 answer:
Choose 1 answer:
(Choice A) The mixture has more than the intended volume and has the intended percent of butterfat.
A
The mixture has more than the intended volume and has the intended percent of butterfat.
(Choice B, Checked) The mixture has the intended volume and has the intended percent of butterfat.
B
The mixture has the intended volume and has the intended percent of butterfat.
(Choice C) The mixture has less than the intended volume and has more than the intended percent of butterfat.
C
The mixture has less than the intended volume and has more than the intended percent of butterfat.
(Choice D) The mixture has the intended volume and has less than the intended percent of butterfat.
D
The mixture has the intended volume and has less than the intended percent of butterfat.

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1 answer
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Answer 1

Bot GPT 4-o mini answered
2 hours ago

To determine what point \( J \) represents in this context, let's analyze the variables and equations provided.

1. **Volume Constraint**: The equation \( x + y = 500 \) represents the constraint that the total volume of whipping cream \( x \) and milk \( y \) must equal \( 500 \, \text{mL} \).

2. **Butterfat Content Equation**: The equation \( 0.30x + 0.02y = 0.12(500) \) represents the condition that the total butterfat content from both the whipping cream and milk must equal the intended butterfat content of the mixture. Here, \( 0.12(500) \) calculates the total amount of butterfat needed for the 500 mL of a final mixture that is 12% butterfat.

Given that point \( J \) is found on line A (the butterfat content equation) and above line B (the total volume equation), we can conclude the following:

- Since point \( J \) is on line A, it satisfies the butterfat content equation, meaning it has the intended percent of butterfat.
- Since point \( J \) is above line B, it implies that the total volume represented by \( x + y \) is greater than \( 500 \, \text{mL} \).

Based on this analysis, point \( J \) represents:

**(Choice A)** The mixture has more than the intended volume and has the intended percent of butterfat.