Problem Solving

A certain theater has 100 balcony seats. For every $2 increase in the price of a balcony seat above $10, 5 fewer seats will be sold. If all the balcony seats are sold when the price of each seat is $10, which of the following could be the price of a balcony seat if the revenue from the sale of balcony seats is $1,360 ?
(A) $12
(B) $14
(C) $16
(D) $17
(E) $18



Hi, The answer is C) but again I could not figure out... my attempt was...
xy=1360
10x+2=100y-5
but could not get to the answer...

We can construct an equation like the form below since the product of
balcony ticket price and total number of tickets = 1360

(10 + 2n) * (100 - 5n) = 1360
Solving for n we get 3 or 12

n = 3 => price of balcony ticket = 10 + 2*3 = 16$

A certain theater has 100 balcony seats. For every $2 increase in the price of a balcony seat above $10, 5 fewer seats will be sold. If all the balcony seats are sold when the price of each seat is $10, which of the following could be the price of a balcony seat if the revenue from the sale of balcony seats is $1,360 ?
(A) $12
(B) $14
(C) $16
(D) $17
(E) $18

If seats are sold for $10, 100 will be sold
If seats are sold for $12, 95 will be sold (total rev = 95*12 = 1140)
If seats are sold for $14, 90 will be sold (total rev = 90*14 = 1260)
If seats are sold for $16, 85 seats will be sold (total rev = 85*16=1360)

Hence Answer = C=16

Reverse engineering works!