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.

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.
Transcript text: 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. \$ $\square$ Submit
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Solution

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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.

Step 1: Establish the Proportional Relationship

The cost of the corporate team-building event is directly proportional to the number of attendees. We can express this relationship mathematically as: C1A1=C2A2 \frac{C_1}{A_1} = \frac{C_2}{A_2} where C1C_1 and A1A_1 are the cost and number of attendees for the first scenario, and C2C_2 and A2A_2 are the cost and number of attendees for the second scenario.

Step 2: Substitute Known Values

From the problem, we know:

  • C1=360C_1 = 360
  • A1=30A_1 = 30
  • A2=33A_2 = 33

We need to find C2C_2. Substituting the known values into the proportion gives: 36030=C233 \frac{360}{30} = \frac{C_2}{33}

Step 3: Solve for C2C_2

Cross-multiplying to solve for C2C_2: C2=36030×33 C_2 = \frac{360}{30} \times 33 Calculating this yields: C2=12×33=396 C_2 = 12 \times 33 = 396

Final Answer

The cost of the corporate team-building event with 33 attendees is \\(\boxed{396}\\).

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