(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...
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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...
(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...
Say you sold the tickets for $14
14 *100= 1400= total revenue
But for every $2 increase you lost five seats. $14-10= $4
$4/2 *5 seats= 10 seats lost, so the revenue lost is 10 seats *$14= 140
1400-140 is the net revenue
So set an equation according to this.
Remember when you’re stuck, pick easy numbers and work backwards.
Step 1) $14*100
In this case, it’s x(100)=total rev
X(100) –((x-10)/2) *(5X)=1360
Just plug and try all the answer choices.
14 *100= 1400= total revenue
But for every $2 increase you lost five seats. $14-10= $4
$4/2 *5 seats= 10 seats lost, so the revenue lost is 10 seats *$14= 140
1400-140 is the net revenue
So set an equation according to this.
Remember when you’re stuck, pick easy numbers and work backwards.
Step 1) $14*100
In this case, it’s x(100)=total rev
X(100) –((x-10)/2) *(5X)=1360
Just plug and try all the answer choices.
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When the price is $10. 100 balcony seats were sold
For every $2 increase in price, % fewer seats were sold
If price of $10 + $2= $12
95 seats will be sold and total revenue =
95*$12 = $1140
If price is $(12+2) = $14
90 will be sold and total revenue =
90*$14 = $1260
If price is $(14+2) =$16
85 seats will be sold and total revenue =
85 * $16 = $1360
Therefore, when the revenue is $1360
the price is $16 per seat.
For every $2 increase in price, % fewer seats were sold
If price of $10 + $2= $12
95 seats will be sold and total revenue =
95*$12 = $1140
If price is $(12+2) = $14
90 will be sold and total revenue =
90*$14 = $1260
If price is $(14+2) =$16
85 seats will be sold and total revenue =
85 * $16 = $1360
Therefore, when the revenue is $1360
the price is $16 per seat.
