# Math Help - Quadratic Worded Problem. HELP.

1. ## Quadratic Worded Problem. HELP.

How do you work this out?

Tickets for a concert are available at two prices. The more expensive ticket is $30 more than the cheaper one. Find the cost of each type of ticket if a group can buy 10 more of the cheaper tickets than the expensive ones for$1800.

2. Originally Posted by amanda.chonghalliday
How do you work this out?

Tickets for a concert are available at two prices. The more expensive ticket is $30 more than the cheaper one. Find the cost of each type of ticket if a group can buy 10 more of the cheaper tickets than the expensive ones for$1800.
An approach:

Let X = cost of expensive ticket, Y = cost of cheap ticket, n = number of expensive tickets that can be bought for \$1800.

Then:

X = Y + 30 .... (1)

nX = 1800 .... (2)

(n + 10)Y = 1800 => nY + 10Y = 1800 .... (3)

Sub (1) into (2): n(Y + 30) = 1800

Expand: nY + 30n = 1800 .... (4)

(4) - (3) => Y = 3n. Sub this into (3):

$(n + 10)(3n) = 1800 \Rightarrow 3n^2 + 30n - 1800 = 0 \Rightarrow n^2 + 10n - 600 = 0 \Rightarrow n = 20$ (the negative solution is discarded since n > 0).

Sub n = 20 into (2): X = 90.

Sub X = 90 into (1): Y = 60.