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A movie theatre rewards its loyal customers by offering them discounts

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New post 17 Jul 2019, 09:09
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Correct answer is C;

Explanation is in the attachment
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New post 17 Jul 2019, 09:10
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IMO-C

First 10# Movies= $50/movie
From 11#- 20# movie= $45/movie
From 21#- 30# movie= $40/movie
From 31#- 40# movie= $35/movie
From 41#- 50# movie= $30/movie
From 51#-60# movie= $25/movie
61#- Any no.= $ 25/movie.

Now , total movie watched= 95#

Amount= 10 x (50+45+40+35+30+25) + (95-60) x 25
= 10 x 3 x 75 + (25 x 35)
= 225 x 10 + (30-5)x(30+5)
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New post 17 Jul 2019, 09:10
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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?


Movie #
1 -10 = 10 x 50
11-20 = 10 x 45
21-30 = 10 x 40
31-40 = 10 x 35
41-50 = 10 x 30
51-60 = 10 x 25
61-95 = 35 x 25.... no further discount after 25

Total dollar amount can be calculated by adding all results above. BUT, we dont want to do any calculations as the answers are not a single number.

We will try to rewrite the answer in the format of the options:

first 6 values have 10 as common so Total of all 7 terms could be written as
(50+45+40+35+30+25) x 10 + 35 x 25

225 x 10 + 35 x 25

This matches with Option C

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


Answer: C. 225×10+(30+5)(30−5)
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New post 17 Jul 2019, 09:12
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The price of:
1) first 10 movies: 10*50
2) second 10 movies: 10*45
3) third 10 movies: 10*40
4) fourth 10 movies: 10*35
5) fifth 10 movies: 10*35
6) sixth 10 movies: 10*25

Let's stop and calculate this part:
Factor out 10 to get --> 10*(50+45+40+35+30+25)=10*225

As John has watched 95 movies and we have calculated the first 60 movies cost, we have to calculate 35 movies cost each costing $25 (per stem 25$ is fixed and does not change after 60 movies)
35*25=(30+5)*(30-5)

Let's sum both parts
10*225+(30+5)*(30-5)

IMO
Ans: C
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New post 17 Jul 2019, 09:13
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I was not able to figure out the series based on the option. So I quickly moved to solve.

1-10 --> 500
11-20 --> 450
21-30 --> 400
31-40 --> 350
41-50 --> 300
51-95 --> 45X25 = 1125

Adding all ==> 3125

Option C satisfies. Hence C is the answer.
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New post 17 Jul 2019, 09:21
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Sequences :

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

i.e. C
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New post 17 Jul 2019, 09:23
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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?

Attachment:
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movies.PNG [ 27.46 KiB | Viewed 141 times ]

A. 200×10+35×25 = $2875
B. 60×25+45×35 = $3075

C. 225×10+(30+5)(30−5) = $3125
D. 225×10+(40+5)(30−5) = $3375
E. 225×10+(40+5)(40−5) = $3825


C is the answer.
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New post 17 Jul 2019, 09:26
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Summation will be

500+400+350+300+250+250+250+250+125=3125

It option C matches this !!

C is the answer

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New post 17 Jul 2019, 09:33
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IMO C

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?

Given, For the first 10 movies, cost = $10×50
For next 10 movies, cost = $10×45
For next 10 movies, cost = $10×40
For next 10 movies, cost = $10×35
For next 10 movies, cost = $10×30
For next 10 movies, cost = $10×25
Total dollar spent on first 60 movies = (500+450+400+350+300+250) = 2250 = 225×10
Total cost of last 35 movies = 35×25 = (30+5)(30−5)
So total amount spent for 95 movies = 225×10+(30+5)(30−5)
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New post 17 Jul 2019, 09:34
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First 50 movies get charged at 50-5(n-1) where n is the set of ten movies John watched, e.g. movies 21-30 will be charged at 50-5(3-1)=40 and movies 41-50 at 50-5(5-1)=30 and any movie beyond the first 50 will be charged a ticket of 25 per movie.

If John watches 95 movies, the cost of movies will be given by:
\(50*10+45*10+40*10+35*10+30*10+25*45\) ==>> \(10(200)+25*45\). Now we can check to see which of the options give us the same result, we will refer to the portion of 10(200) as the "first part" and the 25*45 as the "second part" :

A. \(200×10+35×25\) - Look at the expression, the first part i.e. \(200*10\) is the same as our answer but the second part is \(35*25\) which is not correct.
B. \(60×25+45×35\) - If we factored out the original expression to get 25 in the first part we would have \(80*25+45*25\), now this option is multiplying 20 less in the first part i.e. \(60*25\) instead of \(80*25\), now lets see if multiplying 45 by 35 instead of 25 makes up the difference: \(20*25=500\) (the deficit from the first part) while \(45*10=450\) (the excess from the second part of the expression) we are 50 short then, so this can't be correct either.
C. \(225×10+(30+5)(30−5)\) - In the original expression the first part gave us a value of 2000 whereas first part in this option gives us a value of 2250 which is 250 higher, check to see if the second part is lower by 225, the second part in this option simplifies to \(35*25\) which is 250 lower than \(25*45\) (\(10*25=250\)). So it balances out and yields the same answer as the original expression. Lets check the other two options just to be sure.
D. \(225×10+(40+5)(30−5)\) - First part is 250 higher than original, same as option C, but the second part is the same as the original expression, i.e. \(45*25\) and thus answer will be 250 higher, incorrect.
E. \(225×10+(40+5)(40−5)\) - First part is 250 higher just like options C and D, but second part is 450 higher than original expression, i.e. \(450*35\) instead of \(450*25\) which will be \(45*10=450\) higher than the original answer, incorrect.

Correct option is C.
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New post 17 Jul 2019, 09:37
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The dollar amount paid by John for the 95 movies =
= 1st 10 + 2nd 10 + 3rd 10 + 4th 10 + 5th 10 + 6th 10 + rest 35
\(= (10*50)+(10*45)+(10*40)+(10*35)+(10*30)+(10*25)+(35*25)\)
\(= 10(50+45+40+35+30+25)+(35*25)\)
\(=10*225 + (30+5)*(30-5)\) --> C
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New post 17 Jul 2019, 09:39
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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?

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)

its given: for each 10 movies price reduces from 50 to 25

so for first 60 movies prices are ( 10 x 50 ) + ( 10 x 45 ) +( 10 x 40 ) +( 10 x 35 ) +( 10 x 30 ) +( 10 x 25 )
= 10 x ( 50 + 45 + 40 + 35 + 30 + 25 )
= 10 x 225

for next 35 ( 95 - 60) movies price = 25 X 35

so total price = 10 x 225 + 25 X 35 . Thus ans C
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New post Updated on: 18 Jul 2019, 09:14
Quote:
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+35×25
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)


given: after first 10, each subsequent set of 10 get price reduced by 5, limited to $25 life-time
n=95… amount={10*50+10*45+10*40+10… (notice the pattern)}:
{50(10+9+8+7+6+5)+25(35)}=50(45)+25(35)=2250+25(35)

Answer (C).

Originally posted by exc4libur on 17 Jul 2019, 09:44.
Last edited by exc4libur on 18 Jul 2019, 09:14, edited 1 time in total.
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New post 17 Jul 2019, 09:51
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so the rates will be like below for the 95 days:
10 days-50$
10 days 45$
10 days 40$
10 days 35$
10 days 30$
Remaining days 25$ => 45 days
so total=500+450+400+350+300+25*45 =2000 + 45*25
Option A/D &E goes out of picture immediately as they are greater than above.

B is less than the 2000 $ + 45*25 $ so answer is option C.
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New post 17 Jul 2019, 10:02
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For the first 10 movies, ticket price = 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.
after that, each movie price = 25 per movie

john watch 95 movies

first 10 movies cost = 10*50 = 500

from now on each set of 10 movies reduces by 5 till ticket price equals 25 per movie

set--1 10 movies cost = 10*45
set--2 10 movies cost = 10*40
set--3 10 movies cost = 10*35
set--4 10 movies cost = 10*30
set--5 10 movies cost = 10*25

now 35 movies left each cost 25 per movie = 35*25 = (30+5)(30-5)

cost of above 60 movies = 10(25+30+35+40+45+50) = 10*225

the total cost of 95 movies that he paid = 225*10 + (30+5)(30-5)

C is the answer
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New post 17 Jul 2019, 10:07
For first 10 movies price is 50 x 10 = 500
For next 10 movies price is 45+40+35+30+25+ 25*5 = 300
Price for 80 movies (after first 10 movies) = 300*8 = 2400
Price of last 5 movies = 45+40+35+30+25 = 175

Total price of 95 movies = 500+2400+175 = 3075

B. 60×25+45×35 = 1500 + 1575 = 3075

B is correct.
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New post 17 Jul 2019, 10:30
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First 10 movies - $50
Next10 Till 20 - $45
" Till 30 - $40
" Till 40 - $35
" Till 50 - $30
" Till 60 - $25 and after this no more reductions

So 95 movies implies = 10*(50+45+40+35+25) + 25*35(remaining 35 movies in 25$) = 225*10 + 25*35 --> C
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New post 17 Jul 2019, 10:31
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Given that;

1 - 10 tickets = 50 x 10 = 500
11 - 20 tickets = 45 x 10 = 450
21 - 30 tickets = 40 x 10 = 400
31 - 40 tickets = 35 x 10 = 350
41 - 50 tickets = 30 x 10 = 300
51 - 60 tickets = 25 x 10 = 250

Total cost here = 2250 = 225 x 10

From this point on, the tickets remain constant at $25

therefore, 61 - 95 = 25 x 35 = 1125

Thus, total cost = 225 x 10 + (25 x 35)

This can be re-written as: 225 x 10 + (30 + 5)(30 - 5)

Hence answer choice C.
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New post 17 Jul 2019, 10:32
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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?
Solution:
1st 10 tkts: 10*50
2nd 10 tkts: 10*(50 - 1*5)
3rd 10 tkts: 10*(50 - 2*5)
............................
6th 10 tkts: 10*(50 - 5*5)

Total paid for 6*10 i.e 60 tickets = 10*50 + 10*45 + 10 *40 + .....+ 10 * 25 = 10 * 5 ( 10 + 9 +.....+ 5 ) = 10 * 5 * 6*(10+5)/2= 50*45 = 225 * 10 --(i)
money paid for last 95-60 i.e. 35 tickets = 25 * 35 = (30+5) * (30-5) --(ii)
Total paid for 95 tickets = 225*10 + (30+5) * (30-5) .... adding (i) & (ii)


A. 200×10+35×25
B. 60×25+45×35
C. 225×10+(30+5)(30−5) --> correct
D. 225×10+(40+5)(30−5)
E. 225×10+(40+5)(40−5)
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New post 17 Jul 2019, 11:19
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First 10 moviest at price 50 = 50*10
Second 10 at price 45 = 45*10
.. so it goes till price reaches 25: 10*50+10*45+10*40+10*35+10*30
we are left with 95-50 = 45 movies at price 25. We can rewrite \(45*25\) as \(10*25+35*25\) and as \(10*25 + (30+5)*(30-5)\).

Total equation is therefore as following:
\(10*50+10*45+10*40+10*35+10*30+10*25+35*25 = 10*(50+45+40+35+30+25)+(30+5)*(30-5) = 10*225 + (30+5)*(30-5)\), which is C
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Re: A movie theatre rewards its loyal customers by offering them discounts   [#permalink] 17 Jul 2019, 11:19

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