PS

[jet1445]

1. 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

Ans.C

2.A rainstorm increased the amount of water stored in State J reservoirs from 124 billion gallons to 138 billion gallons. If the storm increased the amount of water in the reservoirs to 82 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?
(A) 9 (B) 14 (C) 25
(D) 30 (E) 44

Ans.E

[Neo2000]

1. 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

Ans.C

Shortest Method
If you looked at the options, you would see that C i.e. $16 is the only option that divides 1360 perfectly.

The longer way would be to find out instantly eliminate D i.e. 17 since the question mentions that for every $2 rise, which means you are looking for even number
Then figure out
12x95 ( since $2 raise meant 5 seats less sold)
14x90
16x85 = 1360
Hence C

2.A rainstorm increased the amount of water stored in State J reservoirs from 124 billion gallons to 138 billion gallons. If the storm increased the amount of water in the reservoirs to 82 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?
(A) 9 (B) 14 (C) 25
(D) 30 (E) 44

Ans.E

If 138billion gallons = 82%
??? = 100%

Once you get that, simply subtract 124billion gallons fm that to get your answer.

[BTGmoderatorRO]

Question 1
Given in the question, number of balcony seats = 100
Also for every $2 increase above $10, 5 fewer seats are sold.

At $10 = price of each Balcony seat,
total revenue = $10 * 100 (i.e all the seats sold) = $1000
similarly, at $2 increase above $10
at $12 = price of each balcony seat,
Total revenue = $12 * 95 (i.e 5 fewer seats sold) = $1140

Now finding a general solution to represent this, we have;
when the price increases by $2 ---> making 'x' a variable form (o---> ∞) [i.e 0<x<∞]

it gives a '5x' fewer seats sold. Thus giving the equation for the total revenue to be { TR = $ (10+2x) * (100-5x) } --------(i)
given a TR of $1360 in the equation above to k now the price of each balcony seats, we have,
1360= (10+2x) (100-5x)
1000-50x+200x-10x^2 = 1360
-10x^2 +150x-360 = 0 -----------------------*
multiplying through by -1 and dividing through by 10, we have,
x^2 -12x+36=0
(x-3)(x-12)=0
x=3 or x=12.

if x=3, price of each balcony seat from eqn (i) = $ (10+2x) = $16
if x=12, price of each balcony seat= $(10+2x) = $34

The price could be $16 or $34. But $16 is given in option C, so we go for $16.
NOTE: The two prices given above can be confirmed equal to the TR of $1360 if the values of 'x' are substituted into TR equation (i).


Question 2
Rainstorm increased the amount of water stored in a reservoir from 124 billion gallons --> 138 billion gallons
Now, given the storm increased the water in the reservoir to 82% of the total capacity,
(82/100) * x = 138
letting x = Total volume of tank
82x = 13800
x= 168 billion gallons (approximately)

prior to the storm, the approximate billion gallons of water short of the total volume is 168-124= 44 billion gallons

[Scott@TargetTestPrep]

1. 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

Ans.C

Let n be the number of $2 increases in the price above the original $10 price. Then, the number of people attending is 100 - 5n and the price of the ticket is 10 + 2n. We have the following equation:
(100 - 5n)(10 + 2n) = 1360
1000 - 50n + 200n - 10n^2 = 1360
-10n^2 + 150n - 360 = 0
Dividing both sides by -10, we have:
n^2 - 15n + 36 = 0
(n - 3)(n - 12) = 0
n = 3 or n = 12
We see that the price could either be 10 + 2(3) = $16 or 10 + 2(12) = $34. However, since only $16 is given in the answer choices, $16 is the correct answer.
Answer: C

[Scott@TargetTestPrep]

2.A rainstorm increased the amount of water stored in State J reservoirs from 124 billion gallons to 138 billion gallons. If the storm increased the amount of water in the reservoirs to 82 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?
(A) 9 (B) 14 (C) 25
(D) 30 (E) 44

Ans.E

We are given that the water increased from 124 billion gallons to 138 billion gallons. We also know that 138 billion gallons is 82% of the total capacity. Let’s translate this information into an equation, where T = total capacity. We translate the sentence "138 billion gallons is 82% of total capacity" as 138 = (0.82)T, remembering that "is" means "equals" and "of" means "multiply."

However, we are told to APPROXIMATE. So, instead of using the equation 0.82T = 138, we can instead use 0.8T = 136. Note that I chose 136 because I know that it is divisible by 8, but you could just as easily use 138 and ignore the decimal values. Now we need to solve for T.

T = 136/0.8
T = 1360/8
T = 170

The total capacity is approximately 170 billion gallons. It follows that the reservoirs were approximately 170 – 124 = 46 billion gallons short of capacity prior to the storm.

From our approximated answer, we see that answer choice E (44) is closest.

Answer: E