Question
The case of 12 bottles of shampoo holds a total of 126 ounces. If each bottle of shampoo contains the same amount, which represents the total volume of shampoo in ounces, y, of any number of bottles, x?
12 y = 126
y = (StartFraction 12 Over 126 EndFraction) x
Volume of Shampoo
On a coordinate plane, the x-axis is labeled number of bottles and the y-axis is labeled total volume (in ounces). A line goes through points (1, 10) and (4, 42).
Volume of Shampoo
On a coordinate plane, the x-axis is labeled number of bottles and the y-axis is labeled total volume (in ounces). A line goes through points (1, 10) and (40, 3.8).
12 y = 126
y = (StartFraction 12 Over 126 EndFraction) x
Volume of Shampoo
On a coordinate plane, the x-axis is labeled number of bottles and the y-axis is labeled total volume (in ounces). A line goes through points (1, 10) and (4, 42).
Volume of Shampoo
On a coordinate plane, the x-axis is labeled number of bottles and the y-axis is labeled total volume (in ounces). A line goes through points (1, 10) and (40, 3.8).
Answers
Answered by
GPT-4o mini
Given the problem statement, we can break it down step by step to understand the relationship between the number of bottles of shampoo (x) and the total volume of shampoo in ounces (y).
1. **Understanding the Problem**:
- We have 12 bottles that together hold 126 ounces of shampoo.
- To find the amount of shampoo per bottle (y), we can divide the total volume by the number of bottles:
\[
y = \frac{126 \text{ ounces}}{12 \text{ bottles}} = 10.5 \text{ ounces per bottle}
\]
2. **Relationship Between Variables**:
- The formula that relates the total volume of shampoo (y) in ounces to the number of bottles (x) can be expressed as:
\[
y = 10.5x
\]
where \( y \) is the total volume in ounces and \( x \) is the number of bottles.
3. **Analyzing the Coordinate Plane**:
- If we plot points based on the relationship derived:
- At \( x = 1 \), \( y = 10.5 \times 1 = 10.5 \)
- At \( x = 4 \), \( y = 10.5 \times 4 = 42 \)
- Thus, the points \( (1, 10.5) \) and \( (4, 42) \) should lie on the line defined by \( y = 10.5x \).
4. **Comparison with Other Provided Data**:
- The mention of line going through points \( (1, 10) \) and \( (4, 42) \) indicates that either the points may not be consistent with the equation derived or represent a different situation.
- There's also a mention of points \( (1, 10) \) and \( (40, 3.8) \), which seems inconsistent with the derived relationship.
5. **Conclusions**:
- The equation \( y = 10.5x \) represents the total volume of shampoo in ounces based on the number of bottles.
- The linear equation can be plotted to see the linear relationship between the two variables.
- To accurately reflect the issue with the points given, it may suggest that a typographical error exists in reporting those coordinates.
If there are any further clarifications or questions about the relationships or the points plotted, feel free to ask!
1. **Understanding the Problem**:
- We have 12 bottles that together hold 126 ounces of shampoo.
- To find the amount of shampoo per bottle (y), we can divide the total volume by the number of bottles:
\[
y = \frac{126 \text{ ounces}}{12 \text{ bottles}} = 10.5 \text{ ounces per bottle}
\]
2. **Relationship Between Variables**:
- The formula that relates the total volume of shampoo (y) in ounces to the number of bottles (x) can be expressed as:
\[
y = 10.5x
\]
where \( y \) is the total volume in ounces and \( x \) is the number of bottles.
3. **Analyzing the Coordinate Plane**:
- If we plot points based on the relationship derived:
- At \( x = 1 \), \( y = 10.5 \times 1 = 10.5 \)
- At \( x = 4 \), \( y = 10.5 \times 4 = 42 \)
- Thus, the points \( (1, 10.5) \) and \( (4, 42) \) should lie on the line defined by \( y = 10.5x \).
4. **Comparison with Other Provided Data**:
- The mention of line going through points \( (1, 10) \) and \( (4, 42) \) indicates that either the points may not be consistent with the equation derived or represent a different situation.
- There's also a mention of points \( (1, 10) \) and \( (40, 3.8) \), which seems inconsistent with the derived relationship.
5. **Conclusions**:
- The equation \( y = 10.5x \) represents the total volume of shampoo in ounces based on the number of bottles.
- The linear equation can be plotted to see the linear relationship between the two variables.
- To accurately reflect the issue with the points given, it may suggest that a typographical error exists in reporting those coordinates.
If there are any further clarifications or questions about the relationships or the points plotted, feel free to ask!
There are no human answers yet. A form for humans to post answers is coming very soon!