An online database charges $35 an hour during the day and $15.50 an hour at night. If a research company paid $350 for 12 hours of use, which system of equations could be used to determine the number of hours charged at the day rate (d) and at the night rate (n)?

Homework Help: Questions and Answers: An online database charges $35 an hour during the day and $15.50 an hour at night. If a research company paid $350 for 12 hours of use, which system of equations could be used to determine the number of hours charged at the day rate (d) and at the night rate (n)?

Answer:

To solve this problem, we need to set up a system of equations based on the information provided.

Given:

1. The total cost for 12 hours of use is $350.
2. The cost during the day is $35 per hour.
3. The cost at night is $15.50 per hour.
4. The total number of hours used is 12.

Define variables:

• Let d be the number of hours charged at the day rate.
• Let n be the number of hours charged at the night rate.

Set up the equations:

1. The total hours equation: d + n = 12
2. The total cost equation: 35d + 15.5n = 350

System of equations:

d + n = 12

35d + 15.5n ​= 350​

These equations can be used to determine the number of hours charged at the day rate and the night rate.

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