Question
The table below shows the cost at a popular theme park with a minimum of tickets for 4 days.
Number of days cost($)
4. 890
5. 1055.
6. 1220.
the cost per day is $___.
the initial cost is $____.
Number of days cost($)
4. 890
5. 1055.
6. 1220.
the cost per day is $___.
the initial cost is $____.
Answers
GPT-4o mini
To find the cost per day and the initial cost, we can analyze the costs given for different numbers of days.
1. **Cost per day**:
- For 4 days: \( \frac{890}{4} = 222.5 \)
- For 5 days: \( \frac{1055}{5} = 211 \)
- For 6 days: \( \frac{1220}{6} = 203.33 \)
The cost per day decreases as the number of days increases. However, to find a consistent rate, we can work with the changes in total cost:
- The cost for 1 additional day from 4 to 5 days is \( 1055 - 890 = 165 \).
- The cost for 1 additional day from 5 to 6 days is \( 1220 - 1055 = 165 \).
Thus, the cost per day can be considered to average around \( 211 \) (as measured in 5-day stay) or \( 203.33 \) for a 6-day stay. However, the most typical way to derive a consistent cost per day is to use the most logical fixed rate over the first few days, typically ignoring the initial fixed fees.
2. **Initial cost**:
- The initial cost is usually inferred from the cost of the first few days.
- If we consider the cost for 4 days ($890) as including both an initial fee and the additional days' costs, we can find the estimates:
Let’s assume the initial cost (fixed) is **X** and the cost per day is **Y**.
- For 4 days:
\( X + 4Y = 890 \)
- For 5 days:
\( X + 5Y = 1055 \)
From these equations, you can isolate the variable \(Y\):
1. Subtract the first equation from the second:
\[
(X + 5Y) - (X + 4Y) = 1055 - 890
\]
\[
Y = 165
\]
2. Plug the value of \(Y\) back into the first equation:
\[
X + 4(165) = 890
\]
\[
X + 660 = 890
\]
\[
X = 230
\]
So, summarizing the results:
- The cost per day is approximately: **$165**
- The initial cost is: **$230**
Final answers:
- The cost per day is **$165**.
- The initial cost is **$230**.
1. **Cost per day**:
- For 4 days: \( \frac{890}{4} = 222.5 \)
- For 5 days: \( \frac{1055}{5} = 211 \)
- For 6 days: \( \frac{1220}{6} = 203.33 \)
The cost per day decreases as the number of days increases. However, to find a consistent rate, we can work with the changes in total cost:
- The cost for 1 additional day from 4 to 5 days is \( 1055 - 890 = 165 \).
- The cost for 1 additional day from 5 to 6 days is \( 1220 - 1055 = 165 \).
Thus, the cost per day can be considered to average around \( 211 \) (as measured in 5-day stay) or \( 203.33 \) for a 6-day stay. However, the most typical way to derive a consistent cost per day is to use the most logical fixed rate over the first few days, typically ignoring the initial fixed fees.
2. **Initial cost**:
- The initial cost is usually inferred from the cost of the first few days.
- If we consider the cost for 4 days ($890) as including both an initial fee and the additional days' costs, we can find the estimates:
Let’s assume the initial cost (fixed) is **X** and the cost per day is **Y**.
- For 4 days:
\( X + 4Y = 890 \)
- For 5 days:
\( X + 5Y = 1055 \)
From these equations, you can isolate the variable \(Y\):
1. Subtract the first equation from the second:
\[
(X + 5Y) - (X + 4Y) = 1055 - 890
\]
\[
Y = 165
\]
2. Plug the value of \(Y\) back into the first equation:
\[
X + 4(165) = 890
\]
\[
X + 660 = 890
\]
\[
X = 230
\]
So, summarizing the results:
- The cost per day is approximately: **$165**
- The initial cost is: **$230**
Final answers:
- The cost per day is **$165**.
- The initial cost is **$230**.