system of equations and matrice

Question

In order to choose the most appropriate musical to perform next, you visit the box office after the opening weekend. The theater you work for has a total of 500 seats and sells three different types of tickets:

1. adult tickets for $8
2. senior citizen tickets for$7
3. child tickets for $5

On the last day of opening weekend, Sunday, the total ticket sales were $1,626. The box office states that they sold half of the seats in the theater and that there was thirty more children than adults.

Answer 1

I think question is well worded as seniors are not be counted in adults ( Seniors and adults are taken as independent variables

Let A be the number of adult tickets sold, at $8 each

Let S be the number of senior tickets sold,at $7 each

Let C be the number of child tickets sold,at $5 each

So 8A +7S + 5C=1626 EQ 1

Now as the total tickets sold = 250

so, A+S +C= 250 Eq 2

C= A+30 Eq3

So Eq 2 Becomes

2A +S=250-30 =220 Eq 4

and Eq 1 becomes

13A+7S = 1476 Eq 5

Multiply Eq 4 by 7

Thus 14A +7S =1540 Eq 6

Solving Eq 5 and 6

A = 64, Adults

S=220-128 =92 , seniors

and C= 250-156= 94, Children

Answer 2

Hello! I'm not sure what the question is because there isn't one listed in your post, so I will help you set this up.

Let A be the amount of adult tickets sold, and they are $8

Let S be the amount of senior tickets sold, and they are $7

Let C be the amount of child tickets sold, and they are $5

So we have the equation:

250 = A + S + C (Equation 1)

the 250 comes from the theater only selling half of the seats in the theater, which is 500 total.

We also have the equation:

1626 = 8A + 7S + 5C (equation 2)

This equation comes from:

the total ticket sales = $8 * (# of adult tickets) + $7 * (# of senior tickets) + $5 * (# of child tickets)

Finally we have the equation:

C= A + 30 (equation 3)

because the number of child tickets are thirty more than the number of adult tickets.