Question

A concert organizer anticipates selling 4,000 tickets and that a quarter of these will be sold at 20% reduction of original price. He needs to make $60,000 in ticket receipts. How much must a full price ticket be?

Answer 1

$ 15.79

Explanation:

Let x be the price of full ticket,

∵ Total number of tickets = 4000,

Quarter of 4000 tickets =
`(4000)/(4)` = 1000,

Remaining tickets = 4000 - 1000 = 3000,

Since, if the price of each ticket is reduced by 20%,

Then the new price of each ticket = (100 - 20)% of x

= 80% of x

= 0.80x,

According to the question,

The total price of quarters of ticket + total price of remaining tickets = $ 60000

= 0.80x × 1000 + x × 3000 = 60,000

800x + 3000x = 60,000

3800x = 60,000

⇒ x ≈ 15.79

Hence, the price of full ticket is approximately $ 15.79.