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!