Answer:
x = 8.57 However, since the number of coffee mugs the manager purchased must be a whole number, the only possible value for x is 8. Therefore, the manager purchased 8 coffee mugs.
Explanation:
Let x be the number of coffee mugs the manager purchased. We know that the manager purchased a total of 41 coffee mugs and key chains, so the number of key chains he purchased is 41 - x. We also know that each coffee mug costs $8.50 and each key chain costs $2.50, so the total cost of the coffee mugs is $8.50 * x and the total cost of the key chains is $2.50 * (41 - x).
We can set up the following equation to represent the information given in the problem:
$8.50x + $2.50(41 - x) = $132.50
We can then solve this equation for x to find the number of coffee mugs the manager purchased. First, we need to distribute the $2.50 on the right side of the equation:
$8.50x + $2.50 * 41 - $2.50x = $132.50
Next, we can combine like terms on both sides of the equation:
$6x - $2.50x = $132.50 - $2.50 * 41
Finally, we can solve for x by dividing both sides of the equation by $6 - $2.50:
x = (132.50 - $2.50 * 41) / ($6 - $2.50)
Substituting the given values into the equation, we get:
x = (132.50 - $2.50 * 41) / (6 - 2.50)
x = (132.50 - 102.50) / (6 - 2.50)
x = 30 / 3.50
x = 8.57