Chapter 6.5, Problem 12PPS

To determine

To write and solve the system of equations.

Answer to Problem 12PPS

Individual tickets: 149

Couples’ tickets: 111

Explanation of Solution

Given:

Number of individual tickets is 38 more than couples’ tickets.

Calculation:

Let x be the number of individual tickets and y be the number of couples’ tickets.

From the table, the price of individual and the couples’ tickets is given.

  $\Rightarrow 3x+3y=\mathrm{780..................}(1)$

Also, given that the number of individual tickets sold is 38 more than couples’ tickets.

  $\Rightarrow x=y+\mathrm{38..................}(2)$

Substitute the value of x in equation (1).

  $\begin{array}{l}\Rightarrow 3(y+38)+3y=780\\ \Rightarrow 3y+114+3y=780\\ \Rightarrow 6y=666\\ \Rightarrow y=111\end{array}$

Substitute the value of y in equation (2)

  $\Rightarrow x=111+38=149$

Conclusion:

Therefore, the number of individual tickets sold is 149 and the number of couples’ tickets sold is 111.