Question

Five pounds of rice at a store cost $6.50. Rice seasoning cost $1.00 per bottle.

Use the Ray tool to graph the total cost of rice and bottle of seasoning, C, vs pounds of rice, p, at this store.
a
What is the answer?


Okay I have a graph. On the bottom it says Rice (Ib) the numbers are 1 2 3 4 5 6 7 8 9 10. Now on the side the number are like 0.5 then 1 then 1.2 then 2.5 the 3 and so forth it is a pattern of the decimals.

Answer 1

To calculate the total cost, \( C \), of purchasing \( p \) pounds of rice and a bottle of seasoning, we can use the cost information provided:

1. The cost of rice is $6.50 for 5 pounds. Therefore, the cost per pound of rice, \( r \), is:
\[
r = \frac{6.50}{5} = 1.30 \text{ dollars per pound}
\]

2. The cost of one bottle of seasoning remains constant at $1.00.

The total cost \( C \) as a function of pounds of rice \( p \) can be expressed as:
\[
C(p) = 1.30p + 1.00
\]

### Graphing the Equation
1. **X-axis** (Rice in pounds, \( p \)): This ranges from 1 to 10 pounds.
2. **Y-axis** (Total cost, \( C \)): We need to calculate the total cost for different values of \( p \).

### Calculations for Different Values of \( p \):
- For \( p = 1 \):
\[
C(1) = 1.30(1) + 1.00 = 2.30
\]
- For \( p = 2 \):
\[
C(2) = 1.30(2) + 1.00 = 3.60
\]
- For \( p = 3 \):
\[
C(3) = 1.30(3) + 1.00 = 4.90
\]
- For \( p = 4 \):
\[
C(4) = 1.30(4) + 1.00 = 6.20
\]
- For \( p = 5 \):
\[
C(5) = 1.30(5) + 1.00 = 7.50
\]
- For \( p = 6 \):
\[
C(6) = 1.30(6) + 1.00 = 8.80
\]
- For \( p = 7 \):
\[
C(7) = 1.30(7) + 1.00 = 10.10
\]
- For \( p = 8 \):
\[
C(8) = 1.30(8) + 1.00 = 11.40
\]
- For \( p = 9 \):
\[
C(9) = 1.30(9) + 1.00 = 12.70
\]
- For \( p = 10 \):
\[
C(10) = 1.30(10) + 1.00 = 14.00
\]

### Summary of Points to Plot:
- (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)

### Plotting the Graph
- Plot these points on your graph, where the x-axis (pounds of rice) ranges between 1 and 10 and the y-axis (total cost) includes values from about 2.20 to 14.00.
- Connect the points with a straight line, since the relationship is linear.

### Conclusion
The graph \( C \) vs. \( p \) will be a straight line starting from (1, 2.30) and increasing linearly to (10, 14.00). The slope of the line represents the cost per additional pound of rice, which is $1.30, while the y-intercept (the cost when no rice is purchased) is $1.00, which is the cost of the seasoning.