manager purchased a total of 24 coffee mugs and key chains. Each coffee mug cost $9.75, and each key chain costs $3.75. If the manager spent a total of $204.00, how many coffee mugs did the manager purchase?
Let x be the number of coffee mugs the manager purchased.
Therefore, the number of key chains the manager purchased is 24 - x.
The cost of x coffee mugs is 9.75x.
The cost of 24 - x key chains is 3.75(24 - x).
The total cost of coffee mugs and key chains is 9.75x + 3.75(24 - x).
Since the manager spent a total of $204.00, we can write the equation:
9.75x + 3.75(24 - x) = 204.00
Expanding the equation, we get:
9.75x + 90 - 3.75x = 204.00
Combining like terms, we get:
6x + 90 = 204.00
Subtracting 90 from both sides, we get:
6x = 204.00 - 90
6x = 114.00
Dividing both sides by 6, we get:
x = 114.00 / 6
x = <<19=19>>19
The manager purchased 19 coffee mugs. Answer: \boxed{19}.