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. $12B. $14C. $16 D. $17E. $18

Answer:The correct option is C) $16.Step-by-step explanation:Consider the provided information.Let R1 = $1000 revenue if price per seat is $10 and number of seats are 100.Let R2 = $1360 revenue if price increase every time by $2 and 5 lesser number of seats sold that every time.  Hence, for R2,x is the number of seat increase by $2.n is the number of times 5 lesser seats are sold when each time the price is increased by $2.The revenue increased by = $1360-$1000 = $360Now,  x = n since every time the price is increased, lesser number of seats are sold and this is attributed to the increased revenue.The number of times the price is increased by $2 is 2x.The number of times 5 lesser seats are sold is 5n.2x × 5n = 36010xn = 360xn = 36As mentioned above, x = nHence x² = 36Therefore, x =  6Neglect the negative value of  x, as the price is increased, Thus, $6 should be increased in $10.The new price during is = 10+6 = $16.Hence, the correct option is C) $16.