To graph the total cost \( C \) (in dollars) versus the pounds of rice \( p \), we need to find the cost equation based on the information you provided.
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Cost of Rice: The cost of 5 pounds of rice is $6.50, so the cost per pound of rice \( r \) can be calculated as: \[ r = \frac{6.50}{5} = 1.30 \text{ dollars per pound} \]
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Cost of Seasoning: Each bottle of rice seasoning costs $1.00. Assuming you buy one bottle regardless of the amount of rice you purchase, this cost is a fixed cost.
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Total Cost Equation: The total cost \( C \) for \( p \) pounds of rice, including the cost of seasoning, can be expressed as: \[ C = 1.30p + 1.00 \]
Now, let's find the cost at different pound values of rice to plot the points.
- For \( p = 1 \): \[ C = 1.30(1) + 1.00 = 2.30 \]
- For \( p = 2 \): \[ C = 1.30(2) + 1.00 = 3.60 \]
- For \( p = 3 \): \[ C = 1.30(3) + 1.00 = 4.90 \]
- For \( p = 4 \): \[ C = 1.30(4) + 1.00 = 6.20 \]
- For \( p = 5 \): \[ C = 1.30(5) + 1.00 = 7.50 \]
- For \( p = 6 \): \[ C = 1.30(6) + 1.00 = 8.80 \]
- For \( p = 7 \): \[ C = 1.30(7) + 1.00 = 10.10 \]
- For \( p = 8 \): \[ C = 1.30(8) + 1.00 = 11.40 \]
- For \( p = 9 \): \[ C = 1.30(9) + 1.00 = 12.70 \]
- For \( p = 10 \): \[ C = 1.30(10) + 1.00 = 14.00 \]
The points you can plot are:
- \( (1, 2.30) \)
- \( (2, 3.60) \)
- \( (3, 4.90) \)
- \( (4, 6.20) \)
- \( (5, 7.50) \)
- \( (6, 8.80) \)
- \( (7, 10.10) \)
- \( (8, 11.40) \)
- \( (9, 12.70) \)
- \( (10, 14.00) \)
Locating (1, 2.30) on Your Graph:
From the graph you described:
- The horizontal axis represents pounds of rice (with increments of 1).
- The vertical axis represents the total cost \( C \) (with decimal values).
To locate the point \( (1, 2.30) \):
- Move horizontally to \( 1 \) on the bottom axis (pounds of rice).
- Then move vertically to \( 2.30 \) on the side axis, which is between \( 2.0 \) and \( 2.5 \).
This point should be slightly above \( 2.0 \) and below \( 2.5 \). You can plot this point and continue to plot the other points similarly to visualize the relationship.
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