SOLUTION: Lun ho stadium sells 2,200 tickets for a concert. It sells a quarter of them at a 20% discount and further 10% at a 40% discount. How much must it change for tickets if it wants to

Question 1165985: Lun ho stadium sells 2,200 tickets for a concert. It sells a quarter of them at a 20% discount and further 10% at a 40% discount. How much must it change for tickets if it wants to generate an income of $40,000?

Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
total number of tickets sold is 2200.
.25 * 2200 = 550 tickets sold at 20% discount.
(2200 - 550) * .10 = 165 tickets sold at 40% discount.
(2200 - 550 - 165) = 1485 tickets sold at full price.

let x equal the full price of a ticket.
you want to generate total income of 40,000.

your equation is:

(1485 * x) + (550 * .8 * x) + (165 * .6 * x) = 40,000
factor out the x to get:
x * (1485 + 550 * .8 + 165 * .6) = 40,000
simplify to get:
2024 * x = 40,000
solve for x to get:
x = 40,000 / 2024 = 19.76284585

if the full price per ticket is 19.76284585, then you will generate 40,000 dollars when 2200 tickets are sold.

total tickets sold is 2200.
25% of these are sold at 20% discount.
a further 10% of these are sold at 40% discount.

the key phrase here is "a further 10%".

i took that to mean the following.

start with 2200.
take 25% of 2200 and subtract it from 2200 to get 2200 - 550 = 1650.
now take 10% of 1650 and subtract it from 1650 to get 1650 - 165 = 1485.

the result is that:
1485 tickets are sold at full price.
550 tickets are sold at 20% discount.
165 tickets are sold at 40% discount.

note that, if you allow the full price to be equal to x, then:

full price = x
20% discount = x - .2 * x = (1 - .2) * x = .8 * x
40% discount = x - .4 * x = (1 - .4) * x = .6 * x

your solution is that the full price of a ticket is equal to 19.76284585.

if you round down to the nearest penny, you will get slightly less than 40,000 (39,9994.24).
if you round up to the nearest penny, you will get slightly more than 40,000 (40,014.48).

if you want to make at least 40,000, then round up.
either way, you're going to be very close.

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The choice of wording in the statement of the problem indeed makes the meaning ambiguous; but I would disagree with the other tutor's interpretation. I believe the meaning is

25% of 2200 = 550 were sold at 80% of basic price
10% of 2200 = 220 were sold at 60% of basic price
65% of 2200 = 1430 were sold at full price

Then

to the nearest cent

In fact at that price the total ticket sales will be pennies short of $40,000; if the $40,000 must be reached, the basic ticket price will need to be (at least) $19.99.

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