Question

multiple choice
the amount of tips (in dollars) servers earn triples on holiday weekends.
which of the following statements about the amounts earned by servers is true?
remember:
\triples\ tells you the server tips are being multiplied by 3.
a the difference between the most a server earns and least a server earns is unchanged on holiday weekends.
b the average amount of tips earned by servers increases by $3 on holiday weekends.
c if the most common tip a server usually earns for serving only a cup of coffee is $1.25, on holiday weeks they will usually earn $3.75.

Explanation:

Step1: Analyze option A

Let the maximum tip be \(M\) and the minimum tip be \(m\). The difference is \(D = M - m\). After tripling, the new maximum is \(3M\) and the new minimum is \(3m\). The new difference is \(3M-3m = 3(M - m)=3D\). So option A is false.

Step2: Analyze option B

Let the tips be \(x_1,x_2,\cdots,x_n\). The average \(\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}\). After tripling, the new average is \(\frac{\sum_{i = 1}^{n}3x_i}{n}=3\frac{\sum_{i = 1}^{n}x_i}{n}=3\bar{x}\). The average is tripled, not increased by \(3\). So option B is false.

Step3: Analyze option C

If the most common tip (mode) is \(x = 1.25\). After tripling (multiplying by \(3\)), the new tip is \(3\times1.25=3.75\).

Answer:

C. If the most common tip a server usually earns for serving only a cup of coffee is $1.25, on holiday weeks they will usually earn $3.75.