The cost of holding a party at a rollerskating rink is a function of n, the number of people in the party. The cost function, C , can be represented with this set of rules:
C(n) = 150 ,0 < n ≤ 12
260, 12 < n ≤ 20
400, 20 < n ≤ 30
The cost of a party with 9 people is $_____
.
The cost of a party with 20 people is $_____
since 9 ≤ 12, that would be C(9) = 150
now do n=20
C(9)=400
To find the cost of a party with 9 people and 20 people, we can use the given cost function, C(n).
1. For a party with 9 people:
- The cost function states that for 0 < n ≤ 12, the cost is $150.
- Since 9 falls within this range, the cost of a party with 9 people is $150.
2. For a party with 20 people:
- The cost function states that for 12 < n ≤ 20, the cost is $260.
- Since 20 falls within this range, the cost of a party with 20 people is $260.
Therefore, the cost of a party with 9 people is $150 and the cost of a party with 20 people is $260.
To find the cost of a party with 9 people, we need to use the given cost function, C(n), and substitute n = 9 into the appropriate rule. Let's break it down into steps:
1. Identify the range that applies to 9 people. Looking at the rules, we can see that 0 < n ≤ 12 applies to 9 people.
2. Substitute n = 9 into the rule C(n) = 150 ,0 < n ≤ 12. Hence, C(9) = 150.
Therefore, the cost of a party with 9 people is $150.
Now, let's find the cost of a party with 20 people using similar steps:
1. Identify the range that applies to 20 people. From the rules, we see that 12 < n ≤ 20 applies to 20 people.
2. Substitute n = 20 into the rule C(n) = 260, 12 < n ≤ 20. Consequently, C(20) = 260.
Hence, the cost of a party with 20 people is $260.