Question

8) Amanda's school is selling tickets to a fall musical. On the first day of ticket sales the school sold 2 adult tickets and 8 student tickets for a total of $140. The school took in $182 on the second day by selling 5 adult tickets and 8 student tickets What is the price each of one adult ticket and one student ticket?​

Answer 1

Let's call the price of one adult ticket "a" and the price of one student ticket "s".

From the information given, we can set up two equations:

2a + 8s = 140 (equation 1)

5a + 8s = 182 (equation 2)

We can solve this system of equations using elimination or substitution.

Let's use elimination. We'll start by multiplying equation 1 by 5 and equation 2 by -2:

10a + 40s = 700 (equation 1, multiplied by 5)

-10a - 16s = -364 (equation 2, multiplied by -2)

Adding these two equations eliminates the "a" term:

24s = 336

Dividing both sides by 24:

s = 14

Now we can substitute this value of "s" into either equation to solve for "a". Let's use equation 1:

2a + 8(14) = 140

2a + 112 = 140

2a = 28

a = 14

So the price of one adult ticket is $14 and the price of one student ticket is