Q:

# Mofor's school is selling tickets to the annual dance competition. On the first day of ticket sales the school sold 7 adult tickets and 6 tickets for a total of $143. The school took in$187 on the second day by selling 4 adult tickets and 13 student tickets. Find the price of an adult ticket and the price of a student ticket.

Accepted Solution

A:
The price of one adult ticket is $11 and the price of one student ticket is$ 11Solution:Given that , Mofor’s school is selling tickets to the annual dance competition.  Let the cost of one adult ticket be $m and the cost of one student tickets be$n.On the first day of ticket sales the school sold 7 adult tickets and 6 tickets for a total of $143. $$\text { Then, } 7 \times \text { cost of one adult ticket }+6 \times \text { cost of one student ticket }=\ 143$$7m + 6n = 143 ------- eqn (1)The school took in$187 on the second day by selling 4 adult tickets and 13 student tickets.  $$\text { Then, } 4 \times \text { cost of one adult ticket}+13 \times \text { cost of one student ticket}=\ 187$$4m + 13n = 187  ------ eqn (2)We have to find the price of an adult ticket and the price of a student ticket.Now, let us solve the equations.Multiply eqn 1 by 428m + 24n = 572  ----- eqn 3Multiply eqn 2 by 728m + 91n = 1309  ---- eqn 4Now subtract eqn 4 from eqn 328m + 24n = 57228m + 91n = 1309(- )--------------------------------------– 67n = - 73767n = 737n = 11Plug in n = 11 in eqn 17m + 66 = 1437m = 143 – 66m = 11Hence, the cost of one adult ticket is $11 and cost of one student ticket is$11