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A movie theatre rewards its loyal customers by offering them discounts

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Re: A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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New post 17 Jul 2019, 11:25
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For the first 10 movies, ticket price is 10*50$. Next 10 movies, it's 10*45$ and so on

Total Price = 10 * 50 +10 * 45+10 * 40+10 * 35+10 * 30+10 * 25 + 35 * 25 = 2250 + 35*25 = 10*225 + (30+5)*(30-5)
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New post 17 Jul 2019, 11:39
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A movie theatre rewards its loyal customers by offering them discounts on the ticket price. For the first 10 movies that a person watches in the movie theatre, the ticket price is $50 per movie. For each subsequent set of 10 movies, the ticket price reduces by $5 per movie till the point where the ticket price equals $25 per movie. The person then gets a lifetime discount and can watch all subsequent movies at a ticket price of $25 per movie. If John watched 95 movies in this movie theatre last year, then the dollar amount that he paid for the tickets of the 95 movies is equivalent to which of the following?

Here,
[(50*10)+(45*10)+(40*10)+(35*10)+(30*10)+(25*10)]+[(25*10)+(25*10)+(25*10)+(25*5)]
= 10 (225) + 25 (35)
= 10 * 225 + (30-5) (30+5)

So, the correct answer choice is (C)
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New post 17 Jul 2019, 11:47
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A movie theatre rewards its loyal customers by offering them discounts on the ticket price. For the first 10 movies that a person watches in the movie theatre, the ticket price is $50 per movie. For each subsequent set of 10 movies, the ticket price reduces by $5 per movie till the point where the ticket price equals $25 per movie. The person then gets a lifetime discount and can watch all subsequent movies at a ticket price of $25 per movie. If John watched 95 movies in this movie theatre last year, then the dollar amount that he paid for the tickets of the 95 movies is equivalent to which of the following?

Ticket price for first 10 movies = $50
For subsequent set of 10 movies prices keep reducing by $5 till it reaches $25. Therefore,
For subsequent 10 movies = $45
next 10 movies = $40.. and so on till next 10 movies = $25...
Total movies till this point will be 60.
From here on ticket price = $25.

Therefore for John, ticket price of 95 movies will be:
10*$50+10*$45+10*$40+10*$35+10*$30+10*$25+35*$25 =
10*(50+45+40+35+30+25) + 35*25 =
10*225+(30+5)(30-5)...This is option C


A. 200×10+35×25
B. 60×25+45×35
C. 225×10+(30+5)(30−5)
D. 225×10+(40+5)(30−5)
E. 225×10+(40+5)(40−5)

Answer Choice: C
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Re: A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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New post 17 Jul 2019, 11:56
Given,

1. Total movies watched by John in the year = 95

2. Cost of first 10 movies for John = 10 * 50 = 500 .... 1

3. Cost of subsequent sets of 10 movies for John = (45 + 40 + 35 + 30 + 25 + 5 * 25)

4. Total number of subsequent sets of 10 movies = 8

5. Cost of subsequnt 8 sets of 10 movies each = 8 * (45 + 40 + 35 + 30 + 25 + 5 * 25)
=> 8 * (5 * (9 + 8 + 7 + 6 + 5) + 5 * 25)
=> 40 * (35 + 25)
=> 40 * 60
=> 2400 .... 2

6. Cost of remaining set of 5 movies as total is 95 = (45 + 40 + 35 + 30 + 25) = 175 .... 3

Adding 1, 2, 3 we get,

=> 500 + 2400 + 175
=> 3075

Now let us check the options,

A. 200×10+35×25 => 2875 => Wrong.

B. 60×25+45×3560×25+45×35 => 3075 => Correct.

C. 225×10+(30+5)(30−5)225×10+(30+5)(30−5) => 3125 => Wrong.

D. 225×10+(40+5)(30−5)225×10+(40+5)(30−5) => 3375 => Wrong.

E. 225×10+(40+5)(40−5) => 3825 => Wrong.

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P.S: I found this to be a very poorly worded question.
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New post 17 Jul 2019, 12:18
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A movie theatre rewards its loyal customers by offering them discounts on the ticket price. For the first 10 movies that a person watches in the movie theatre, the ticket price is $50 per movie. For each subsequent set of 10 movies, the ticket price reduces by $5 per movie till the point where the ticket price equals $25 per movie. The person then gets a lifetime discount and can watch all subsequent movies at a ticket price of $25 per movie. If John watched 95 movies in this movie theatre last year, then the dollar amount that he paid for the tickets of the 95 movies is equivalent to which of the following?

For first 10 movies price is 50
next 10 ---- 45
next 10 ---- 40
next 10 ---- 35
next 10 ---- 30
next 10 ---- 25

Total movies: 60
remaining movies: 95 - 60 = 35

next 35 --- 25

Total amount spent:
50*10 + 45*10 + 40*10 + 35*10 + 30*10 + 25*10 + 25*35
= 10 (50+45+40+35+30+25) + 25*35

If we go through the options we can see option C matches our solution.

We can write the above equation as

10 * 225 + (30+5) * (30-5)

Answer: C

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New post 17 Jul 2019, 12:32
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Total movies watched =95

First 10 movies cost =10(50)
Since , for each subsequent set of 10 movies, the ticket price reduces by $5 per movie till the point where the ticket price equals $25 per movie.

Second 10 movies cost =10(45)
Third 10 movies cost =10(40)
Fourth 10 movies cost =10(35)
Fifth 10 movies cost =10(30)
Sixth 10 movies cost =10(25)

Remaining 35 movies cost 25 each
.: 35(25)
.: Total dollar amount paid = 10(50)+10(45)+10(40)+10(35)+
10(30)+10(25)+35(25) = 225(10) +35(25)

Now 225(10)+35(25)= (225 x 10+(30+5)(30-5))

Answer C

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New post 17 Jul 2019, 12:47
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First 10 movies costs: 10x50
11th to 20th movie is: 10x45
21st to 30th movie is: 10x40
31st to 40th movie is: 10x35
41st to 50th movie is: 10x30
51st to 60th movie is: 10x25
Remaining movies is: 35x25

Total cost of the 95 tickets =10(50+45+40+35+30+25) +35x25
=225x10 + 35x25
Which is the same as
225x10 + (30+5)(30-5)
Hence answer is C.

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New post 17 Jul 2019, 12:48
A movie theatre rewards its loyal customers by offering them discounts on the ticket price. For the first 10 movies that a person watches in the movie theatre, the ticket price is $50 per movie. For each subsequent set of 10 movies, the ticket price reduces by $5 per movie till the point where the ticket price equals $25 per movie. The person then gets a lifetime discount and can watch all subsequent movies at a ticket price of $25 per movie. If John watched 95 movies in this movie theatre last year, then the dollar amount that he paid for the tickets of the 95 movies is equivalent to which of the following?

A. 200×10+35×25200×10+35×25
B. 60×25+45×3560×25+45×35
C. 225×10+(30+5)(30−5)225×10+(30+5)(30−5)
D. 225×10+(40+5)(30−5)225×10+(40+5)(30−5)
E. 225×10+(40+5)(40−5)225×10+(40+5)(40−5)


For first 10 movie.....$50 = 10*50=$500
next 10 movies @ discount of $5 (then price will be 50-5=$45) = 45*=$450
Similarly for another next 10 movies (new price 45-5 = $40) = 40*10 = $400

.
.
for another 10 movies $ 35 = $350
for another 10 movies $ 30 = $300
for another 10 movies $ 25 = $250
here we completed Calculation for 60 movies...for all next movies he will be charged lifetime of $25/movie

movies left = 95-60 = 35
thus now total price =35*25

thus total price he paid = 500+450+400+350+300+(25*45)
which equals as option B

Ans B
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Re: A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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New post 17 Jul 2019, 12:59
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Amount paid by customer for first 10 movies= 10*50=500
Amount paid by customer for 11-20th movie= 10*45=450
Amount paid by customer for 21-30th movie= 10*40=400
Amount paid by customer for 31-40th movie= 10*35=350
Amount paid by customer for 41-50th movie= 10*30=300
Amount paid by customer for 51-95th movie= 45*25=1125

amount that he paid for the tickets of the 95 movies= 500+450+400+350+300+1125=3125

A. 2000+900-25=2875 Incorrect
B. 1500+1600-25=2975 Incorrect
C. 2250+900-25=3125 Correct
D. 2250+1125= 3375 Incorrect
E. 2250+1600-25= 3825 Incorrect

IMO C
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New post 17 Jul 2019, 14:20
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So we have the following:
(50+45+40+35+30)*10 - the cost of movies before we have a lifelong discount.
45*25 - the cost of movies after we have a lifelong discount.

the equation is 200*10 + 45*25

From the first glance there are no identical equations among the possible answers.
But after closer look we will see that option C is identical to our target, because 225*10 is the same as (200+25)*10, so we need extra $250 to our 200*10. And 45*25 is exactly 250 more than 35*25.

The answer is C
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New post 17 Jul 2019, 14:35
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Answer is C

A/Q,
for the first set of 10 movies=10*50
for the 2nd set of 10 movies=10*45
for the 3rd set of 10 movies=10*40
for the 4th set of 10 movies=10*35
for the 5th set of 10 movies=10*30
for the 6th set of 10 movies=10*25
for the rest of the movies=35*25 [Total 95 movies]

Therefore,
10*50+10*45+10*40+10*35+10*30+10*25+25*35
=10(50+45+40+35+30+25)+35*25
=10*225+35*25
=225*10+(30+5)(30-5)

Answer is C
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New post 17 Jul 2019, 14:40
Answer B

Catch in the question is "Subsequent set of 10 movies ", which one can ignore reading fast (i did, so spent bit more time )
rest answer is pretty straight forward with lot of math

First 10 movies: 50*10
Next subsequent set of 10 movies : 45+40+35+30+25 =175, After this each movie at 25 each,so 25*5=125 : 175+125=300
Now this would continue till next 8 sets till we reach 90 movies :
So 300*8 = 2400
For movies 9195 again same rule of 45+40+35+30+25 = 175
Total 2400+ 175+ 500 =3075

Solving options in B you will arrive at solution of 3075 :
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New post 17 Jul 2019, 15:12
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First 10 movies @ $50 per movie = 10 *50 (Note: don't solve at this point because answer choices are not whole numbers)
Next 10 @ $45 = 10*45 (20 movies so far)
Next 10 @ $40 = 10*40 (30 movies so far)
Next 10 @ $35 = 10*35 (40 movies so far)
Next 10 @ $30 = 10*30 (50 movies so far)
Next 10 @ $25 = 10*25 (60 movies so far)
Remaining 35 movies @$25 = 35*25

Total = 10 (50+45+40+35+30+25) + 35*25, --> 10 * 225 + (30+5)(30-5)

Answer choice C
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New post 17 Jul 2019, 17:54
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first 10 movies cost ; 10*50 ; 500
11-20 movies; 45*10; 450
21-30 movies; 40*10 ; 400
31-40 movies; 35*10 ; 350
41-50 movies; 30*100 ; 300
51-95; 25*45; 1125
total ; 2000+1125; 3125
IMO C;
225×10+(30+5)(30−5)
A movie theatre rewards its loyal customers by offering them discounts on the ticket price. For the first 10 movies that a person watches in the movie theatre, the ticket price is $50 per movie. For each subsequent set of 10 movies, the ticket price reduces by $5 per movie till the point where the ticket price equals $25 per movie. The person then gets a lifetime discount and can watch all subsequent movies at a ticket price of $25 per movie. If John watched 95 movies in this movie theatre last year, then the dollar amount that he paid for the tickets of the 95 movies is equivalent to which of the following?

A. 200×10+35×25200×10+35×25
B. 60×25+45×3560×25+45×35
C. 225×10+(30+5)(30−5)225×10+(30+5)(30−5)
D. 225×10+(40+5)(30−5)225×10+(40+5)(30−5)
E. 225×10+(40+5)(40−5)
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New post 17 Jul 2019, 18:10
(50+45+40+35+30)*10 + 25*(95-10*5) = 200*10 + 25*35.

Answer is A
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New post 17 Jul 2019, 18:22
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First set 10 movies - 50*10 = 25*20
Second set 10 movies - 45*10 = 25*18
third set 10 movies - 40*10 = 25*16
Fourth set 10 movies - 35*10 = 25*14
Fifth set 10 movies - 30*10 = 25*12
Sixth set 10 movies - 25*10 = 25*10
remaining 35 movies - 25*35 = 25*35

Total cost = 25* 125 = Our option C

C. 225×10+(30+5)(30−5)= 25*90 + 25*35

So Ans is C

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New post 17 Jul 2019, 18:39
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1) For the first 10 movies that a person watches in the movie theatre, the ticket price is $50 per movie=> 10*50

2) For each subsequent set of 10 movies, the ticket price reduces by $5 per movie till the point where the ticket price equals $25 per movie.
=> 10*45+10*40+10*35+10*30+10*25

John has watched 60 movies so far. Remaining=95-60=35

3) Can watch all subsequent movies at a ticket price of $25 per movie => 35*25

Adding 1,2 and 3-
10*(50+45+40+35+30+25)+35*25
=>10*225+(30+5)(30-5)

Hence option C.
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New post 17 Jul 2019, 19:06
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A movie theatre rewards its loyal customers by offering them discounts on the ticket price. For the first 10 movies that a person watches in the movie theatre, the ticket price is $50 per movie. For each subsequent set of 10 movies, the ticket price reduces by $5 per movie till the point where the ticket price equals $25 per movie. The person then gets a lifetime discount and can watch all subsequent movies at a ticket price of $25 per movie. If John watched 95 movies in this movie theatre last year, then the dollar amount that he paid for the tickets of the 95 movies is equivalent to which of the following?

First 10 tickets Total = 50*10
Next 10 tickets = 45*10
Next 10 tickets = 40*10
Next 10 tickets = 35*10
Next 10 tickets = 30*10

Next 10 tickets = 25*45

Total Amount = 10* (50+45+40+35+30) + 25*45
= 10*200 + 25*45
= 10*200 + 25*(10+35)
= 10*200 + 25*10+ 25*35
= 10*225 + 25*35---------Option C is the correct answer




A. 200×10+35×25

B. 60×25+45×35

C. 225×10+(30+5)(30−5)

D. 225×10+(40+5)(30−5)

E.225×10+(40+5)(40−5)
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New post 17 Jul 2019, 19:30
Tickets are like this:

50 10 10
45 20 10
40 30 10
35 40 10
30 50 10
25 60 10
25 95 35

225 *25 + 35 *25
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New post 17 Jul 2019, 19:50
The price of 1st 10 tickets will be 10*50 =500

For the next tickets the price will be 45,40,35,30,25

The sum of above will be =500+(45+40+35+30+25)==675

No of tickets used until now ==10+5=5

Remaining Tickets =80

We are told that now all tickets will have a value of 25$

Total value of remaining tickets=25*80 ==2000

Total value of all the 95 tickets =2000+675==2675

IMO A.
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Re: A movie theatre rewards its loyal customers by offering them discounts   [#permalink] 17 Jul 2019, 19:50

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