Question

A company rents out 15 food booths and 20 game booths at the county fair. The fee for a food booth is $100 plus $5 per day. The fee for a game booth is $50 plus $7 per day. The fair lasts for 'd' days, and all the booths are rented for the entire time. Write and simplify an expression for the amount in dollars the the company is paid.

Answer 1

To calculate the total amount paid for renting out food and game booths at the county fair, we use the expressions for the cost of each booth type, including their fixed and daily rates. The simplified expression for the total amount paid to the company is $2500 + $215d, where d is the number of days the fair lasts.

Step-by-step explanation:

To write an expression for the amount the company is paid for renting out food and game booths at the county fair, we need to calculate the total cost for each type of booth and then sum them up.

The total cost for the food booths is calculated by taking $100 as the fixed fee for each food booth and adding $5 per day for d days. With 15 food booths, the expression for the total cost of food booths is 15 × ($100 + $5d).

Similarly, for the 20 game booths, we have a fixed fee of $50 per booth and a daily fee of $7 for d days. So, the total cost for game booths is 20 × ($50 + $7d).

By adding both expressions together, we get the total amount paid to the company:

15 × ($100 + $5d) + 20 × ($50 + $7d) = 15 × $100 + 15 × $5d + 20 × $50 + 20 × $7d

$1500 + $75d + $1000 + $140d = $2500 + $215d

Therefore, the simplified expression for the total amount paid to the company is $2500 + $215d.

Answer 2

Given that 15 food booths were rented out for ‘d’ days at $100 plus $5 per day. On the food booths only, the company will earn 15($100+$5d) = $1500 + $75d Given that 20 game booths were rented out for ‘d’ days at $50 plus $7 per day. On the game booths only, the company will earn 20($50 + $7d) = $1000 + $140d
The total amount that the company is paid is therefore, $1500 + $75d + $1000 + $140d = $2500 + $215d