Question

The price of the lunch for 15 people was $\$207.00$ , including a 115 percent gratuity for service. What was the average price per person, excluding the gratuity?
$\begin{align}
  & A.\text{ }\$11.73\\&B.\text{}\$12.00\\&C.\text{}\$13.80\\&D.\text{}\$14.00\\&E.\text{}\$15.87\\\end{align}$

Answer 1

Hint: In this question, we have to find the average price of the lunch per person. Thus, we will use the percentage formula and the basic mathematical rule to get the solution. First, we will change the 115% into decimal form by dividing the number by 100. Then, we will use the formula $\text{actual price of the lunch}\times \text{gratuity of the service=total price of the lunch}$ , where we will substitute the values to get the value of actual price of the lunch. In the last, for the average price, we will divide the actual price by 15, to get the required solution for the problem.

Complete step by step solution:
According to the problem, we have to find the average price of the lunch excluding the gratuity.
Thus, we will use the percentage formula and the basic mathematical rule to get the solution.
The total price of the lunch is equal to $\$207.00$ ----- (1)
Number of people are 15 ----- (2)
Gratuity of the service is equal to 115% ------ (3)
Let the actual price of the lunch is equal to x ------- (4)
Now, we will first convert the percentage into decimal that is we will remove the percentage sign by dividing equation (3) by 100, we get
$\Rightarrow 115%=\dfrac{115}{100}$
Therefore, we get
$\Rightarrow 115%=1.15$ ---------- (5)
Now, we will use the formula $\text{actual price of the lunch}\times \text{gratuity of the service=total price of the lunch}$, that is we will put the value of equation (1), (4), and (5) in the above formula, we get
$\Rightarrow x\times 1.15=\$207.00$
Now, we will divide 1.15 on both sides in the above equation, we get
$\Rightarrow \dfrac{x\times 1.15}{1.15}=\dfrac{\$207.00}{1.15}$
Therefore, we get
$\Rightarrow x=\$180$ --------- (6)
Therefore, we will divide the total number of people and the actual price of lunch, that is equation (6) and (2), we get
$\Rightarrow \text{average price of the lunch=}\dfrac{\$180}{15}$
On further solving the above division, we get
$\Rightarrow \text{average price of the lunch= }\${12}$
Therefore, the average price per person, excluding the gratuity is equal to $\$12$ that is option (B) is correct.

Note: While solving this problem, do step by step calculation, to avoid error and mathematical error. Do not forget to mention the standard units with the solution to get the accurate answer.