Question

The ticket sales at a movie theater were $3,402. Adult tickets are $11, and senior tickets are $8. The number of senior tickets sold was 27 less than twice the number of adult tickets. Determine the number of adult tickets and senior tickets sold.

Answer 1

Adults: 134

Senior: 241

Explanation:

Known

Number of adult tickets sold: x

Revenue from adult tickets: $11x

Number of senior tickets sold: y

Revenue from senior tickets: $8y

From the problem, we found the equation
`y = 2x - 27` and 3,402 = 11x + 8y

Combining the two equation:

`3,402 = 11x + 8(2x-27)\\3,402 = 11x + 16x - 216\\3,402 + 216 = 27x\\27x = 3,618`

Divided both side by 27

`x = 134`

Since

`y = 2x - 27`

Inserting the value of x,

`y = 2(134) -27\\y = 268 - 27\\y = 241`

So, there are 134 adult tickets sold and 241 senior tickets sold.