Question

The drama club at Math Academy High School sold tickets to their end of the year play. On Monday they sold 80 tickets for a total of $426. If each adult ticket cost $6 and student tickets cost $4.50, how many adult tickets did they sell?

A) 44
B) cannot be determined
C) 36
D) 71

Answer 1

Answer: OPTION A

Explanation:

Let be "a" the number of adults tickets they sold and "s" the number student of tickets they sold.

With the information given in the exercise you can set up the following System of equations:

`\left \{ {{a+s=80} \atop {6a+4.5s=426}} \right.`

Use the Elimination method to solve the system of equations:

1. Multiply the first equation by -6.

2. Add the equations.

3. Solve for "s" in order to find its value.

Then:

`\left \{ {{-6a+-6s=-480} \atop {6a+4.5s=426}} \right.\\............................\\-1.5s=-54\\\\s=36`

4. Finally, substitute the value of "s" into the first equation and solve for "a":

`a+36=80\\\\a=80-36\\\\a=44`