Question
Mary Beth likes to go to her local car wash because she is a premier member there. Her membership fee costs $80.00 and that membership allows her to get her car washed for $26.00 every visit.
Fill in the table to find how much it costs for 2, 4, 5, and 8 visits. Use the calculator to help you solve.
Number of visits (v) Cost to get car washed (c) Cost per visit (
v
c
)
2 $
132
4 $
184
5 $
210
8 $
288
Nice!
Now, fill in the table to find the cost per visit. Use the calculator to help you solve.
Number of visits (v) Cost to get car washed (c) Cost per visit (
v
c
)
2 $132 $
66
4 $184 $
46
5 $210 $
42
8 $288 $
36
Nice!
Could the relationship between the number of visits and the cost be proportional?
Number of visits (v) Cost to get car washed (c) Cost per visit (
v
c
)
2 $132 $66.00
4 $184 $46.00
5 $210 $42.00
8 $288 $36.00
The relationship could be proportional.
The relationship could not be proportional.
Fill in the table to find how much it costs for 2, 4, 5, and 8 visits. Use the calculator to help you solve.
Number of visits (v) Cost to get car washed (c) Cost per visit (
v
c
)
2 $
132
4 $
184
5 $
210
8 $
288
Nice!
Now, fill in the table to find the cost per visit. Use the calculator to help you solve.
Number of visits (v) Cost to get car washed (c) Cost per visit (
v
c
)
2 $132 $
66
4 $184 $
46
5 $210 $
42
8 $288 $
36
Nice!
Could the relationship between the number of visits and the cost be proportional?
Number of visits (v) Cost to get car washed (c) Cost per visit (
v
c
)
2 $132 $66.00
4 $184 $46.00
5 $210 $42.00
8 $288 $36.00
The relationship could be proportional.
The relationship could not be proportional.
Answers
GPT-4o mini
To determine if the relationship between the number of visits (v) and the cost to get the car washed (c) is proportional, we can analyze the costs and the corresponding costs per visit.
Given the following cost breakdown:
- Membership fee: $80.00
- Cost per visit: $26.00
**Total Cost (c) Calculation:**
The total cost for any number of visits (v) is calculated as:
\[
c = \text{Membership Fee} + (\text{Cost per Visit} \times \text{Number of Visits})
\]
\[
c = 80 + (26 \times v)
\]
Now calculating for each number of visits:
1. **For 2 visits:**
\[
c = 80 + (26 \times 2) = 80 + 52 = 132
\]
2. **For 4 visits:**
\[
c = 80 + (26 \times 4) = 80 + 104 = 184
\]
3. **For 5 visits:**
\[
c = 80 + (26 \times 5) = 80 + 130 = 210
\]
4. **For 8 visits:**
\[
c = 80 + (26 \times 8) = 80 + 208 = 288
\]
This corresponds with your given costs.
Now let's look at the cost per visit:
**Cost per visit calculation:**
To find the cost per visit, we divide the total cost by the number of visits:
\[
\text{Cost per visit} = \frac{c}{v}
\]
For each number of visits (as calculated):
1. **For 2 visits:**
\[
\text{Cost per visit} = \frac{132}{2} = 66.00
\]
2. **For 4 visits:**
\[
\text{Cost per visit} = \frac{184}{4} = 46.00
\]
3. **For 5 visits:**
\[
\text{Cost per visit} = \frac{210}{5} = 42.00
\]
4. **For 8 visits:**
\[
\text{Cost per visit} = \frac{288}{8} = 36.00
\]
### Conclusion
- **Is the relationship proportional?**
The costs per visit are not constant as the number of visits increases. They change from $66.00 to $36.00, meaning that the cost per visit decreases with more visits.
Therefore, the relationship **could not be proportional**.
Given the following cost breakdown:
- Membership fee: $80.00
- Cost per visit: $26.00
**Total Cost (c) Calculation:**
The total cost for any number of visits (v) is calculated as:
\[
c = \text{Membership Fee} + (\text{Cost per Visit} \times \text{Number of Visits})
\]
\[
c = 80 + (26 \times v)
\]
Now calculating for each number of visits:
1. **For 2 visits:**
\[
c = 80 + (26 \times 2) = 80 + 52 = 132
\]
2. **For 4 visits:**
\[
c = 80 + (26 \times 4) = 80 + 104 = 184
\]
3. **For 5 visits:**
\[
c = 80 + (26 \times 5) = 80 + 130 = 210
\]
4. **For 8 visits:**
\[
c = 80 + (26 \times 8) = 80 + 208 = 288
\]
This corresponds with your given costs.
Now let's look at the cost per visit:
**Cost per visit calculation:**
To find the cost per visit, we divide the total cost by the number of visits:
\[
\text{Cost per visit} = \frac{c}{v}
\]
For each number of visits (as calculated):
1. **For 2 visits:**
\[
\text{Cost per visit} = \frac{132}{2} = 66.00
\]
2. **For 4 visits:**
\[
\text{Cost per visit} = \frac{184}{4} = 46.00
\]
3. **For 5 visits:**
\[
\text{Cost per visit} = \frac{210}{5} = 42.00
\]
4. **For 8 visits:**
\[
\text{Cost per visit} = \frac{288}{8} = 36.00
\]
### Conclusion
- **Is the relationship proportional?**
The costs per visit are not constant as the number of visits increases. They change from $66.00 to $36.00, meaning that the cost per visit decreases with more visits.
Therefore, the relationship **could not be proportional**.