Question

The equations $6x+y=18$ and $5x+2y=22$ represent the fees collected from college concert tickets sales during two class periods. If $x$ represents the cost for each adult ticket and $y$ represents the cost for each student ticket, what is the cost for each student ticket?

• A. Rs. 4
• B. Rs. 7
• C. Rs. 5
• D. Rs. 6

Answer 1

The correct option is D Rs. 6

$x=$ represents the cost for each adult ticket
$y=$ represents the cost for each student ticket
Therefore by solving the given equation,
$6x+y=18$ ----- (1)
$5x+2y=22$ ----- (2)
From equation (1),
$6x=18-y$
$x=\frac{18-y}{6}$
Put the value of $x$ in equation (2),
$5x+2y=22$
$5\left(\frac{18-y}{6}\right)+2y=22$
$905y+12y=132$
$7y=13290$
$y=\frac{42}{7}=6$
So, the cost for each student ticket is Rs. 6