MATH SOLVE

2 months ago

Q:
# 3. Brenda's school is selling tickets to a spring musical. On the first day ofticket sales the school sold 3 senior citizen tickets and 9 child tickets for a totalof $75. The school took in $67 on the second day by selling 8 senior citizentickets and 5 child tickets. What is the price each of one senior citizen ticketand one child ticket?β

Accepted Solution

A:

Answer: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 ticketsLet c = the cost of child ticketsThe number of tickets sold for each type added together equals the sales for each day. Equations below:Day 13s + 9c = $75Solve for s:3s = 75 - 9cs = 25 - 3cDay 28s + 5c = $67By substitution:8(25 - 3c) + 5c = 67200 - 24c + 5c = 67-19c = -133c = -133 / -19 = $7 cost for child tickets.Solve for s:s = 25 - 3cs = 25 - 3(7)s = 25 - 21 = $4 cost for senior citizen tickets.Proofs:Day 13s + 9c = $753(4) + 9(7) = 7512 + 63 = 7575 = 75Day 28s + 5c = $678(4) + 5(7) = 6732 + 35 = 6767 = 67