Question

88 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

If tips triple, the difference between the highest - and lowest - earning servers also triples. For example, if the lowest is $x$ and the highest is $y$, the difference is $y - x$. After tripling, the new difference is $3y-3x = 3(y - x)$. So option A is false.

Step2: Analyze option B

If the original average of tips is $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, after tripling, the new average is $\frac{\sum_{i = 1}^{n}3x_{i}}{n}=3\times\frac{\sum_{i = 1}^{n}x_{i}}{n}=3\bar{x}$. The average amount of tips does not increase by $\$3$, but triples. So option B is false.

Step3: Analyze option C

If the most common tip is $x = 1.25$, when tips triple, the new tip amount is $3x$. Substitute $x = 1.25$ into $3x$, we get $3\times1.25=3.75$. So option C is true.

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 $\$3.75$.