Question

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales

the school sold 1 senior citizen tickets and 13 child ticket for a total of $128. The school took in $166 on
the second day by selling 11 senior citizen tickets and 5 child tickets. Find the price of a senior citizen
ticket and the price of a child ticket.

Answer 1

The Answer is: The cost of senior citizen tickets: $11. The cost of children tickets: 9.

Explanation:

Let s = cost of senior tickets and c = cost of child tickets.

The total dollar amount is equal to the number of senior and adult tickets sold times the amount for each. Equations below:

Day 1:

13c + 1s = $128

Solve for s:

s = 128 - 13c

Day 2

5c + 11s = 166

By substitution, then solve for c:

5c + 11(128 - 13c) = 166

5c + 1408 - 143c = 166

-138c = -1242

c = -1242/-138 = 9 dollars for child tickets.

Solve for s:

s = 128 - 13c

s = 128 - 13(9)

s = 128 - 117 = 11 dollars per senior tickets.

Proofs:

Day 1:

13c + 1s = $128

13(9) + 1(11) =

117 + 11 = 128

128 = 128

Day 2:

5c + 11s = 166

5(9) + 11(11) = 166

45 + 121 = 166

166 = 166