Question

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.

Answer 1

The price of one adult ticket is $ 11 and the price of one student ticket is $ 11

Solution:

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 4

28m + 24n = 572  ----- eqn 3

Multiply eqn 2 by 7

28m + 91n = 1309  ---- eqn 4

Now subtract eqn 4 from eqn 3

28m + 24n = 572

28m + 91n = 1309

(- )--------------------------------------

– 67n = - 737

67n = 737

n = 11

Plug in n = 11 in eqn 1

7m + 66 = 143

7m = 143 – 66

m = 11

Hence, the cost of one adult ticket is $ 11 and cost of one student ticket is $11