Question
At breakfast, a restaurant charges $2 for the first cup of orange juice and then $1 for each refill. Which graph represents this situation?
A graph titled Orange Juice has number of refills on the x-axis and total cost on the y-axis. A line goes through points (0, 1) and (1, 3).
A graph titled Orange Juice has number of refills on the x-axis and total cost on the y-axis. A line goes through points (0, 1) and (1, 2).
A graph titled Orange Juice has number of refills on the x-axis and total cost on the y-axis. A line goes through points (0, 2) and (1, 4).
A graph titled Orange Juice has number of refills on the x-axis and total cost on the y-axis. A line goes through points (0, 2) and (1, 3).
A graph titled Orange Juice has number of refills on the x-axis and total cost on the y-axis. A line goes through points (0, 1) and (1, 3).
A graph titled Orange Juice has number of refills on the x-axis and total cost on the y-axis. A line goes through points (0, 1) and (1, 2).
A graph titled Orange Juice has number of refills on the x-axis and total cost on the y-axis. A line goes through points (0, 2) and (1, 4).
A graph titled Orange Juice has number of refills on the x-axis and total cost on the y-axis. A line goes through points (0, 2) and (1, 3).
Answers
Answered by
GPT-4o mini
To analyze the cost structure described:
- The first cup of orange juice costs $2.
- Each refill costs $1.
Let's break it down mathematically:
1. **Starting Cost**: The cost of the first cup is $2 (when no refills are purchased, i.e., 0 refills, the total cost is $2).
2. **Cost of Refills**: For each refill, you add $1 to the total cost.
Therefore, the total cost \( C \) based on the number of refills \( r \) can be expressed as:
\[ C = 2 + r \]
- If you have 0 refills:
\[ C = 2 + 0 = 2 \]
- If you have 1 refill:
\[ C = 2 + 1 = 3 \]
- If you have 2 refills:
\[ C = 2 + 2 = 4 \]
Now looking at the options:
1. A graph that goes through points (0, 1) and (1, 3) does not match because \( C(0) = 2 \) not 1.
2. A graph that goes through points (0, 1) and (1, 2) does not match because \( C(0) = 2 \) not 1.
3. A graph that goes through points (0, 2) and (1, 4) matches since:
- When \( r = 0 \), \( C = 2 \) (first cup only)
- When \( r = 1 \), \( C = 3 \) (first cup plus 1 refill), and \( C = 4 \) when \( r = 2 \).
4. A graph that goes through points (0, 2) and (1, 3) also matches because:
- When \( r = 0 \), \( C = 2 \)
- When \( r = 1 \), \( C = 3 \) (first cup plus 1 refill).
Therefore, both the third and fourth options are correct representations of the situation described with the first cup price and the refills. However, the graph that goes through (0, 2) and (1, 3) only reflects refills accurately as it showcases the linear relationship derived from the formula \( C = 2 + r \) more directly in terms of refills versus total cost.
Ultimately, the correct answer should be the graph that goes through (0, 2) and (1, 3).
- The first cup of orange juice costs $2.
- Each refill costs $1.
Let's break it down mathematically:
1. **Starting Cost**: The cost of the first cup is $2 (when no refills are purchased, i.e., 0 refills, the total cost is $2).
2. **Cost of Refills**: For each refill, you add $1 to the total cost.
Therefore, the total cost \( C \) based on the number of refills \( r \) can be expressed as:
\[ C = 2 + r \]
- If you have 0 refills:
\[ C = 2 + 0 = 2 \]
- If you have 1 refill:
\[ C = 2 + 1 = 3 \]
- If you have 2 refills:
\[ C = 2 + 2 = 4 \]
Now looking at the options:
1. A graph that goes through points (0, 1) and (1, 3) does not match because \( C(0) = 2 \) not 1.
2. A graph that goes through points (0, 1) and (1, 2) does not match because \( C(0) = 2 \) not 1.
3. A graph that goes through points (0, 2) and (1, 4) matches since:
- When \( r = 0 \), \( C = 2 \) (first cup only)
- When \( r = 1 \), \( C = 3 \) (first cup plus 1 refill), and \( C = 4 \) when \( r = 2 \).
4. A graph that goes through points (0, 2) and (1, 3) also matches because:
- When \( r = 0 \), \( C = 2 \)
- When \( r = 1 \), \( C = 3 \) (first cup plus 1 refill).
Therefore, both the third and fourth options are correct representations of the situation described with the first cup price and the refills. However, the graph that goes through (0, 2) and (1, 3) only reflects refills accurately as it showcases the linear relationship derived from the formula \( C = 2 + r \) more directly in terms of refills versus total cost.
Ultimately, the correct answer should be the graph that goes through (0, 2) and (1, 3).