Questions: The corporate team-building event will cost 360 if it has 30 attendees. If there are 33 attendees, how much will the corporate team-building event cost? Assume the relationship is directly proportional.

Solution Steps

To solve this problem, we need to understand that the cost of the event is directly proportional to the number of attendees. This means that if the number of attendees increases, the cost increases at the same rate. We can set up a proportion to find the new cost when there are 33 attendees.

The cost of the corporate team-building event is directly proportional to the number of attendees. We can express this relationship mathematically as: \[ \frac{C_1}{A_1} = \frac{C_2}{A_2} \] where \(C_1\) and \(A_1\) are the cost and number of attendees for the first scenario, and \(C_2\) and \(A_2\) are the cost and number of attendees for the second scenario.

From the problem, we know:

• \(C_1 = 360\)
• \(A_1 = 30\)
• \(A_2 = 33\)

We need to find \(C_2\). Substituting the known values into the proportion gives: \[ \frac{360}{30} = \frac{C_2}{33} \]

Cross-multiplying to solve for \(C_2\): \[ C_2 = \frac{360}{30} \times 33 \] Calculating this yields: \[ C_2 = 12 \times 33 = 396 \]

Final Answer