Question

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 1

The correct option is C) $16.

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 = $360

Now, 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 = 360

10xn = 360

xn = 36

As mentioned above, x = n

Hence x² = 36

Therefore, x = 6

Neglect 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.