Question

a local community theather 240 tickets for Saturday nights performance they sold 180 more st full price then the discount tickets which system of equations can be used to model the situation

Answer 1

Question:

The local community theater sold a total of 240 tickets for Saturday night’s performance. They sold 180 more full-price tickets than discount tickets. Which system of equations can be used to model this situation?

Answer:

`x = 180 + y`

`x + y = 240`

Explanation:

Given

`Tickets = 240`

Represent the number of full price with x and discounted price with y.

From the question:

x = 180 more than y

So:

`x = 180 + y`

Also, a total of 240 were sold.

So:

`x + y = 240`

Hence, the equations are:

`x = 180 + y`

`x + y = 240`

Solving further;

Substitute 180 + y for x in
`x + y = 240`

`180 + y + y = 240`

`180 + 2y = 240`

Solve for 2y

`2y = 240 - 180`

`2y = 60`

Divide through by 2

`y = 30`

Recall that:
`x = 180 + y`

`x = 180 + 30`

`x = 210`

Hence:

Full Price = 210

Discounted = 30