Chapter 6, Problem 9PFA

To determine

To find: The number of student- tickets sold by members of band at Jason’s high school.

Answer to Problem 9PFA

C is the correct option.

Explanation of Solution

Given information:

The members of band raised $ 1500 and sold 400 tickets. The price of adult ticket is $5 each and that of student ticket $3. The number of student tickets sold is (only one digit is correct):

A 150 B 175 C 250 D 750

Method used:

According to given conditions a system of equations is obtained and then solved.

Calculations:

Let x and y be the number of adult and student tickets sold by members of the band.

Since, total 400 tickets were sold, therefore,

  $x+y=400$  ...... (1)

The total fund raised is $1500, therefore,

  $5x+3y=400$  ...... (2)

Now, multiplying equation (1) by 5 and subtracting from equation (2)

  $\left(5x+3y\right)-5\left(x+y\right)=1500-\left(5\times 400\right)$

  $\Rightarrow 5x+3y-5x-5y=1500-2000$

  $\Rightarrow \cancel{5x}+3y-\cancel{5x}-5y=-500$

  $\Rightarrow -2y=-500$

  $\Rightarrow y=\frac{-500}{-2}=250$

Thus, total students tickets sold were 250.

Hence, C is the correct option.

Conclusion:

C is the correct option.