Question

The price of lunch for \[{\text{15}}\] people was \[{\text{\$ 207}}{\text{.00}}\], including the \[{\text{15}}\]percent gratuity for service. What was the average price per person excluding the gratuity ?
A. \[{\text{\$ 11}}{\text{.73}}\]
B. \[{\text{\$ 12}}{\text{.00}}\]
C. \[{\text{\$ 13}}{\text{.80}}\]
D. \[{\text{\$ 14}}{\text{.00}}\]
E. \[{\text{\$ 15}}{\text{.87}}\]

Answer 1

Hint: Firstly using percentage and proportion method we calculate the cost of lunch excluding gratuity, we can also find the cost for \[{\text{15}}\]using unitary method and then calculate the its average for \[{\text{15}}\]persons.

Complete step by step answer:

Given, the price of lunch for \[{\text{15}}\] people was \[{\text{\$ 207}}{\text{.00}}\], including the \[{\text{15}}\]percent gratuity for service.
As by applying unitary method,
\[
  {\text{15person}} \to {\text{207}} \\
  {\text{1person}} \to \dfrac{{{\text{207}}}}{{{\text{15}}}} \\
 \]
So, first of all we need to calculate the \[{\text{15}}\]percent of \[{\text{\$ 207}}{\text{.00}}\] which can be given as
\[
   \Rightarrow {\text{\$ 207 $\times$ }}\dfrac{{{\text{15}}}}{{{\text{100}}}} \\
   \Rightarrow {\text{\$ 31}}{\text{.05}} \\
 \]
Now we need \[{\text{15}}\]percent less amount of \[{\text{\$ 207}}{\text{.00}}\] which is calculated as
\[
   \Rightarrow {\text{\$ (207 - 31}}{\text{.05)}} \\
   \Rightarrow {\text{\$ 175}}{\text{.95}} \\
 \]
Now , the above amount is without gratuity and is to be divided among \[{\text{15}}\] person, to obtain it for per person, so it can given as
Similarly by applying unitary method,
\[
  {\text{15person}} \to 175.95 \\
  {\text{1person}} \to \dfrac{{175.95}}{{{\text{15}}}} \\
 \]
\[
   \Rightarrow \dfrac{{{\text{\$ 175}}{\text{.95}}}}{{{\text{15}}}} \\
   \Rightarrow {\text{\$ 11}}{\text{.73}} \\
 \]
Hence, the average price of lunch excluding the gratitude is \[{\text{\$ 11}}{\text{.73}}\]
Hence, option (a) is our required correct answer.

Note: In mathematics, a percentage is a number or ratio that represents a fraction of 100. Proportion says that two ratios (or fractions) are equal. The average value is the mean value of all the numbers, it is easy to calculate, just add all the numbers and divide it by the total number of numbers added. As we know the amount of the bulk and so we have to calculate it for the individual using the unitary method. As the given amount is including gratuity and so exclude it using a percentage proportion as shown.