Question

Write a system of equations to model the problem below. Then show the steps to solve your system.

Answer 1

Answer:

Price of adult ticket = x = $13

Price of student ticket = y = $6

Step-by-step explanation:

Let Price of adult ticket = x

Price of student ticket = y

Now, making equations:

On the first day of ticket sales the school sold 6 adult tickets and 7 student tickets for a total of $120. The equation will be:

$6x+7y=120$

The school took in $168 on the second day by selling 12 adult tickets and 2 student tickets. The equation will be:

$12x+2y=168$

Now, solving the equations simultaneously to find values of x and y.

Let:

$6x+7y=120--eq(1)\\12x+2y=168--eq(2)$

Multiply eq(1) by 12 and then subtract both equations

$12x+14y=240\\12x+2y=168\\-\:\:\:-\:\:\:\:\:\:\:\:\:-\\--------\\12y=72\\y=\frac{72}{12}\\y=6$

So, we get value of y: y=6

Now, Put value of y in equation 1 to find value of x

$12x+2y=168\\Put\:y=6\\12x+2(6)=168\\12x+12=168\\12x=168-12\\12x=156\\x=\frac{156}{12}\\x=13$

So, we get value of x: x=13

The answer would be:

Price of adult ticket = x = $13

Price of student ticket = y = $6