Question

A high school musical production sells student tickets for \[\$ 5\] each and adult tickets for \[\$ 8\] each. If the ratio of adult to student tickets purchases is 3:1, what is the average income per ticket sold?
A. $5.50$
B. $5.75$
C. $6.50$
D. $7.25$

Answer 1

Hint: The purchases are given in the ratio, so assume that the ratio could be the number and add them to find the total number of tickets, then according to the tickets purchases, find the total income of the adults and the students. To find the average income per ticket, divide the total income by the total student tickets purchases.

Complete step-by-step answer:
The price of the student tickets sell by musical production is \[p = \$ 5\]
The price of the adult tickets sell by musical production is \[P = \$ 8\]
The ratio of the purchases of adult tickets to the student tickets is \[3:1\]
The total number of tickets will be
\[\begin{array}
t = 3 + 1\\
 = 4
\end{array}\]
Let the total purchases of the adult tickets is 3 then the total price is
\[\begin{array}
x = 3 \times 8\\
 = \$ 24
\end{array}\]
Let the total purchases of the student tickets is 1 then the total price is
\[\begin{array}
y = 1 \times 5\\
 = \$ 5
\end{array}\]
The total income of the tickets purchased by adults and students is
\[\begin{array}
z = 24 + 5\\
 = \$ 29
\end{array}\]
The equation to find the average income per ticket sold is
\[I = \dfrac{z}{t}\]
Substitute the values in the above equation, then we will get
\[\begin{array}
I = \dfrac{z}{t}\\
 = \dfrac{{29}}{4}\\
 = \$ 7.25
\end{array}\]
Therefore, the average income of the tickets solved is\[\$ 7.25\], it means that the option (D) is correct.
So, the correct answer is “Option D”.

Note: Don’t get confused while assuming the ratios as the total tickets purchased, as the prices are provided in dollars, there is no need to convert dollars to rupee, we should be aware about the process of finding the total income per student. To find it, every time, the total income should be in the numerator and the total purchases should be in the denominator.