Chapter 6.4, Problem 34PFA

To determine

To find the cost of a student ticket

Answer to Problem 34PFA

$12

Explanation of Solution

Given:

	Adult tickets	Student tickets	Total cost(in $)
Seana	3	2	84
Mikayla	2	5	100

Calculation:

Let x be the cost of adult tickets and y be the cost of student tickets.

Given that, Seana sold 3 adult tickets and 2 students for $84.

  $\Rightarrow 3x+2y=\mathrm{84........................}(1)$

Also, Mikayla sold 2 adult tickets and 5 student tickets for $100

  $\Rightarrow 2x+5y=\mathrm{100......................}(2)$

Multiply equation (1) with 2 and equation (2) with 3,

  $\Rightarrow 6x+4y=\mathrm{168........................}(3)$

  $\Rightarrow 6x+15y=\mathrm{300......................}(4)$

Subtract equation (3) from equation (4),

  $\begin{array}{l}\Rightarrow (6x+15y)-(6x+4y)=300-168\\ \Rightarrow 15y-4y=132\\ \Rightarrow 11y=132\\ \Rightarrow y=12\end{array}$

Substitute the value of y in equation (1),

  $\begin{array}{l}\Rightarrow 3x+2(12)=84\\ \Rightarrow 3x+24=84\\ \Rightarrow 3x=60\\ \Rightarrow x=20\end{array}$

Conclusion:

Therefore, the cost of student ticket is $12.