3. Brenda's school is selling tickets to a spring musical. On the first day of

ticket sales the school sold 3 senior citizen tickets and 9 child tickets for a total

of $75. The school took in $67 on the second day by selling 8 senior citizen

tickets and 5 child tickets. What is the price each of one senior citizen ticket

and one child ticket?

The Answer is that Senior Citizen Tickets cost: $4 and Child tickets cost: $7.

Step-by-step explanation:

Let s = the cost of senior citizen tickets

Let c = the cost of child tickets

The number of tickets sold for each type added together equals the sales for each day. Equations below:

Day 1

3s + 9c = $75

Solve for s:

3s = 75 - 9c

s = 25 - 3c

Day 2

8s + 5c = $67

By substitution:

8 (25 - 3c) + 5c = 67

200 - 24c + 5c = 67

-19c = - 133

c = - 133 / - 19 = $7 cost for child tickets.

Solve for s:

s = 25 - 3c

s = 25 - 3 (7)

s = 25 - 21 = $4 cost for senior citizen tickets.

Proofs:

Day 1

3s + 9c = $75

3 (4) + 9 (7) = 75

12 + 63 = 75

75 = 75

Day 2

8s + 5c = $67

8 (4) + 5 (7) = 67

32 + 35 = 67

67 = 67