Question
An internet cafe charges $4, plus $3 for every additional hour of using the internet. What is the maximum number of hours that internet can be used for $50?
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10
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15
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8
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14
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10
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15
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8
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14
Answers
GPT-4o mini
To determine the maximum number of hours that can be used for $50 at the internet cafe, we start with the initial charge and the hourly rate.
1. The initial charge is $4.
2. The additional cost per hour is $3.
Let's define the number of hours used after the first hour as \( h \). The total cost can be calculated as follows:
\[
\text{Total Cost} = 4 + 3h
\]
To find the maximum \( h \) for a total cost of $50, we set the equation:
\[
4 + 3h \leq 50
\]
Now, we will isolate \( h \):
1. Subtract 4 from both sides:
\[
3h \leq 50 - 4
\]
\[
3h \leq 46
\]
2. Divide both sides by 3:
\[
h \leq \frac{46}{3}
\]
\[
h \leq 15.33
\]
Since \( h \) represents whole hours, we take the greatest integer less than or equal to 15.33, which is 15.
Now, we include the initial charge:
Total hours used = \( 1 + h = 1 + 15 = 16 \) hours.
However, we should double-check since the options provided might refer to only additional hours:
If \( h = 15 \), with 1 hour accounted for the initial fee, the total number of hours with the additional hour considered should be \( 1 + 15 = 16 \).
But the total cost calculation should still confirm:
Total cost = \( 4 + 3 \times 15 = 4 + 45 = 49 \), which is within the budget of $50.
Hence under the strict interpretation of max hours used with $50:
- 1 hour already accounted for (thus can only pay for 14 additional at $3), the answer would thus be:
The maximum number of hours that can be used for $50 while guided through options given accurately points to **15** hours is the correct maximum choice:
### Thus, the answer is 15.
1. The initial charge is $4.
2. The additional cost per hour is $3.
Let's define the number of hours used after the first hour as \( h \). The total cost can be calculated as follows:
\[
\text{Total Cost} = 4 + 3h
\]
To find the maximum \( h \) for a total cost of $50, we set the equation:
\[
4 + 3h \leq 50
\]
Now, we will isolate \( h \):
1. Subtract 4 from both sides:
\[
3h \leq 50 - 4
\]
\[
3h \leq 46
\]
2. Divide both sides by 3:
\[
h \leq \frac{46}{3}
\]
\[
h \leq 15.33
\]
Since \( h \) represents whole hours, we take the greatest integer less than or equal to 15.33, which is 15.
Now, we include the initial charge:
Total hours used = \( 1 + h = 1 + 15 = 16 \) hours.
However, we should double-check since the options provided might refer to only additional hours:
If \( h = 15 \), with 1 hour accounted for the initial fee, the total number of hours with the additional hour considered should be \( 1 + 15 = 16 \).
But the total cost calculation should still confirm:
Total cost = \( 4 + 3 \times 15 = 4 + 45 = 49 \), which is within the budget of $50.
Hence under the strict interpretation of max hours used with $50:
- 1 hour already accounted for (thus can only pay for 14 additional at $3), the answer would thus be:
The maximum number of hours that can be used for $50 while guided through options given accurately points to **15** hours is the correct maximum choice:
### Thus, the answer is 15.