Chapter 6, Problem 20MCQ

To determine

To find the number of adult’s tickets and number student tickets.

Answer to Problem 20MCQ

The number of tickets sold for adult are 160.

The number of tickets sold for student are 125.

So, option D is correct.

Explanation of Solution

Given information : Given:

The cost of the ticket for the adult is $ 4

The cost of the ticket for the student is $ 1

A total of 285 tickets were sold for the $765

Let the number of tickets sold for adult are x .

The number of tickets sold for student are y

So according to the question:

Number of adult tickets + Number of student tickets= 285

  $x+y=285$ ....Equation 1

Also according to the question:

The cost of adult ticket $\times$ number of adult tickets + The cost of student ticket $\times$ number of student tickets = 765

  $4\times x+1\times y=765$

  $\Rightarrow 4x+y=765$ ....Equation 2

Subtracting Equation 2 from Equation 1:

  $\begin{array}{l}x+y=285\\ 4\times x+1\times y=765\\ (4x+y)-(x+y)=765-285\\ \Rightarrow 4x+y-x-y=480\\ \Rightarrow 3x=480\\ \Rightarrow x=\frac{480}{3}\\ \Rightarrow x=160\end{array}$

Putting the value of x in Equation 1, we get:

  $\begin{array}{l}160+y=285\\ \Rightarrow y=285-160\\ \Rightarrow y=125\end{array}$

So the number of tickets sold for adult are 160.

The number of tickets sold for student are 125.

So option D is correct.