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.
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.
\$ $\square$
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Solution
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:
A1C1=A2C2
where C1 and A1 are the cost and number of attendees for the first scenario, and C2 and A2 are the cost and number of attendees for the second scenario.
Step 2: Substitute Known Values
From the problem, we know:
C1=360
A1=30
A2=33
We need to find C2. Substituting the known values into the proportion gives:
30360=33C2
Step 3: Solve for C2
Cross-multiplying to solve for C2:
C2=30360×33
Calculating this yields:
C2=12×33=396
Final Answer
The cost of the corporate team-building event with 33 attendees is \\(\boxed{396}\\).