A company rents out 17 food booths and 22 game booths at the county fair. The fee for a food booth is $175 plus $10 per day. The fee for a game booth is $50 plus $9 per day. The fair lasts for d days, and all the booths are rented for the entire time. Enter a simplified expression for the amount, in dollars, that the company is paid. The expression is
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Ct = 4075 + 368d

Step-by-step explanation:

Function Models

A company rents out food booths and game booths at the county fair.

For a food booth, the company charges a fixed fee of $175 and a variable fee of $10 per day. If d is the number of days, then the charges for a food booth are:

Cf = 175 + 10d

Similarly, the company charges $50 plus $9 per day for a game booth, thus the total charges are:

Cg = 50 + 9d

If all the booths are rented for the entire time, the total amount the company is paid for 17 food booths and 22 game booths is:

Ct = 17Cf + 22Cg

Substituting:

Ct = 17(175 + 10d) + 22(50 + 9d)

Operating:

Ct = 2975 + 170d + 1100 + 198d

Simplifying:

Ct = 4075 + 368d