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A movie theatre rewards its loyal customers by offering them discounts

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New post 17 Jul 2019, 20:15
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----10 Movies-----||-------10 Movies----------||-------10 Movies------ ---||--||--|| -------10 Movies------||---------10 Movies---------||
ticket price = 50 || price reduces by 5=45 || price reduces by 5=40 ||--||--|| price until price =25 || lifetime price =25 ||

95 Movies
10 Movies = 10* 50 = 500
10 Movies = 10 *45 = 450
10 Movies = 10 *40 = 400
10 Movies = 10 *35 = 350
10 Movies = 10 *30 = 300
10 Movies = 10 *25 = 250
10 Movies = 10 *25 = 250
10 Movies = 10 *25 = 250
10 Movies = 10 *25 = 250
5 Movies = 5 *25 = 150

Then is the part to actually map it to the answer choice; only C matches
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New post 17 Jul 2019, 21:14
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Given: Rate of first 10 movies=$50; Rate of next 10 movies(no.11 to no.20)=$45, Rate of next 10 movies(no.21 to no.30)= $40, Rate of next 10 movies(no.31 to no. 40)=$35, Rate of next 10 mobies(no.41 to no.50)=$30 and rate of movies afterwards=$25
Total no. of movies watched by John=95
Now,
Cost of first 10 movies= 10*$50
Cost of movies from no.11 to no.20(i.e next 10 movies)=10*$45
Cost of movies from no.21 to no.30(i.e next 10 movies)=10*$40
Cost of movies from no.31 to no.40(i.e next 10 movies)=10*$35
Cost of movies from no.41 to no.50(i.e next 10 movies)=10*$30
Cost of movies from no.51 to no.60(i.e next 10 movies)=10*$25
Cost of movies from no.61 onwards(i.e no.61 to no.95)= 30*$25

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

Answer: C
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New post 17 Jul 2019, 21:16
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Customer paid for 95 movies:

First 10 movies - 10*$50
Second 10 movies - 10*$45
Third 10 movies - 10*$40
Fourth 10 movies - 10*$35
Fifth 10 movies - 10*$30
Sixth 10 movies - 10*$25
Seventh 10 movies - 10*$25
Eighth 10 movies - 10*$25
Ninth 10 movies - 10*$25
Last 5 movies - 5*$25
Total: 45*$25+50*$40(average of $30, $35, $40, $45, $50)=$3125, customer paid for 95 movies. Let's see which answer yields 3125.


A. 200×10+35×25 = 2875 NO
B. 60×25+45×35 = 3075 NO
C. 225×10+(30+5)(30−5) = 3125 YES
D. 225×10+(40+5)(30−5) = 3375 NO
E. 225×10+(40+5)(40−5) = 3825 NO

Answer is C
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New post 17 Jul 2019, 21:24
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Let us see the pattern of pricing of movie tickets:

First 10 - $50 each -> 10 * $50
Next 10 - $45 each -> 10 * $45
Next 10 - $40 each -> 10 * $40
Next 10 - $35 each -> 10 * $35
Next 10 - $30 each -> 10 * $30
Next 10 - $25 each -> 10 * $25
Next N - $25 each -> N * $25

John watches 95 movies: 10 + 10 + 10 + 10 + 10 + 10 + N = 95 => N = 35

Total price of tickets = 10*($50 + $45 + $40 + $35 + $30 + $25) + N*$25
=>10*(225) + 35*25
=>225 * 10 + (30 + 5)*(30-5)

Answer C
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New post 17 Jul 2019, 21:41
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first set of 10 tickets :- 10*50
second set of 10 tickets :- 10*45
third set of 10 tickets :- 10*40
fourth set of 10 tickets :- 10*35
fifth set of 10 tickets :- 10*30
sixth set of 10 tickets :- 10*25
Total sum of 6 set (60 movies) of tickeys:-2250

for next 35 movies , the cost will be :- 35*25

Total cost :- 2250+35*25
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New post 17 Jul 2019, 22:35
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1-10 : $50
11-20:$45
21-30:$40
31-40:$35
41-50:$30
>50:$25

Since, John watched 95 movies, his total expenses= 45*25+ 10(30+35+40+45+50) =45*25+10*200=$3125

Verify options,

A. 200×10+35×25 =2000+875, Incorrect
B. 60×25+45×35= 1500+1575,Incorrect
C. 225×10+(30+5)(30−5)= 2250+875=3125, Correct

Correct Ans: C
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New post 17 Jul 2019, 22:58
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John has watched 95 movies till now.

Ticket price for movies are as per following:

1-10 movies : 50*10 = 500 (ticket price starts from 50per movie and it will reduce by 5 per movies for each subsequent set 10 movies.)
11-20 movies : 45*10 = 450
21-30 movies : 40*10 = 400
31-40 movies : 35*10 = 350
41-50 movies : 30*10 = 300
51-60 movies : 25*10 = 250
61-95 movies : 25*35 = (30+5)(30-5)

If we add all of these : 2250 + (30+5)(30-5) = 225*10 + (30+5)(30-5)

So, ANSWER: C
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New post 17 Jul 2019, 23:24
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Price of first 10 movie tickets @ 50 ,Total Cost 50 *10 = 500
Price of next 10 movie tickets 45 ,Total Cost 45 *10 = 450
Price of next 10 movie tickets @ 40 ,Total Cost 40 *10 = 400
Price of next 10 movie tickets @ 35 ,Total Cost 35 *10 = 350
Price of next 10 movie tickets 30 ,Total Cost 30 *10 = 300
Total price of 50 tickets = 2000

Rest all 45 tickets will cost 25, Total cost - 25 * 45 = 1125
Total Cost - 1125 + 2000 = 3125


Option C is same as this - 225 *10 + 35 *25 = 3125
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New post 17 Jul 2019, 23:58
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The initial price of the ticket for the first 10 movies is $50. For the next 10 movies the price will drop by $5. We will have have 5 such drops untill we pay $25.

So \(10*50+10*45+10*40+10*35+10*30+10*25\) is the price for the first \(60\) tickets, if simplified \(10*(50+45+40+35+30+25)\) or \(225*10\)

For the rest 35 tickets we pay by \($25\) or \(35*25\).

Is summed \(225*10+35*25\)

Hence C
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New post 18 Jul 2019, 00:19
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0-10 movies 10*50=500
11-20 movies 10*45=450
21-30 movies 10*40=400
31-40 movies 10*35=350
41-50 movies 10*30=300
51-95 movies 45*25=1125, all added 3125 (C)
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New post 18 Jul 2019, 00:55
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For the 95 movies, we can break down the logic as follows:
10*50 + 10*45 + 10* 40 + 10*35 + 10*30 + 10*25 => 2250
So till now 60 movies got completed.
For the remaining 35 movies:
35*25 => 875

Adding all the values=> 3125
We get that only option C is equal to 3125.

IMO the answer is C.

Please hit kudos if you like the solution.
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New post 18 Jul 2019, 01:33
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For every 10 movies watched, a loyal customer gets discount of 5$ until ticket price reaches 25$. First set of 10 movies cost 50$ each (500 in sum), second set 45$ per each out of 10 movies watched (450), ....... 350+300+250 (50 movies were watched so far). Other 45 movies will be charged 25$. Total sum paid 500+450+400+250+300+250*55=3125.
It is C
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New post 18 Jul 2019, 01:50
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Cost of 1st set of 10 movies = 10*50
Cost of next set of 10 movies = 10*45
Cost of next set of 10 movies = 10*40
Cost of next set of 10 movies = 10*35
Cost of next set of 10 movies = 10*30
Cost of next set of 10 movies = 10*25
So, cost of 60 movies = 10*(50 + 45 + 40 + 35 + 30 + 25) = 225*10

Cost of remaining 35 movies = 25$ each = 35*25

So, total cost of 95 movies = 225*10 + 35*25
= 225x10 + (30+5)x(30-5)

IMO Option C

Pls Hit kudos if you like the solution

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New post 18 Jul 2019, 03:12
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I manually counted and got C, 3125. (I counted every 10 tickets and multiplied by its price 50, 45,40,35,30,35,25,25,25. Last 5 movies also multiplied by 25)
Answer - C
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New post 18 Jul 2019, 03:26
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price reduces by $5 per movie till the point where the ticket price equals $25 per movie.

First 10 - $50
Next 10 - $45
10 - $40
10 - $35
10 - $30
Remaining - $25

First 50 tickets would cost - 10*50 + 10*45 + 10*40 + 10*35 + 10*30 = 2000
Remaining 45 at 25 = 45*25 = 1125
Total = 3125

Among the options,
C. 225×10+(30+5)(30−5)
is the only option which sums to 3125.

Option C.
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New post 18 Jul 2019, 03:42
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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
200×10+35×25

B.
60×25+45×35
60×25+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)

Solution:Now as per the statement
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 follwoing situation arises:

10*50
10*45
10*40
10*35
10*30
10*25
sum of all above=10*225

Now if John watched 95 movies then as per above details given the remaining movies to be watched are 35 25 each.

Hence,the totl amount paid for total 95 movies=10*225+35*25
Therefore C is the answer IMO
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New post 18 Jul 2019, 03:54
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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)

Solution:
The total number of movies that john watched is 95
For the First 10 movies , The cost is $50,
For the next 10, it will be 50+5 i.e 45
another 10, it's 40,
another 10, it's 35
another 10, it's 30
another 10, it's 25 so we have our final price of $25 per movie, note that the cost won't go down any further and $25 will be fixed. so till here, the total cost is 10 X 225
Hence for remaining 35 movies, the cost is going to be $25 per movie, i.e 35 X 25

Therefore, we can form the equation, 225 X 10 + 35 X 25 which is equal to option C

Answer is C
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New post 18 Jul 2019, 04:28
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Tickets => Price

0-10 => $50
11-20 => $45
21-30 => $40
31-40 => $35
41-50 => $30
51-60 => $25
61-95 => $25

{ 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) + (35*25)
= Option (C)
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A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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New post 18 Jul 2019, 04:53
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Question: 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?

\[
\begin{matrix}
Set & Cost & = & (#Terms)(Cost) & = & Total Cost \\
1-10 & 50 & = & (10)(50)& = & $500 \\
11-20 & 45 & = & (10)(45)& = & $450\\
21-30 & 40 & = & (10)(40)& = & $400\\
31-40 & 35 & = & (10)(35)& = & $350\\
41-50 & 30 & = & (10)(30)& = & $300\\
51-60 & 25 & = & (10)(25)& = & $250\\
61-95 & 25 & = & (35)(25) & = & $875\\
\end{matrix}
\]

\(\text{Sum of tickets }1-60\):
\(= 500+450+400+350+300+250\)
\(= 2250 \implies (225)(10)\)

\(\text{Sum of tickets } 61-95\):
\(= (35)(25) \implies (30+5)(30-5)\)

Correct Answer: C. (225×10)+(30+5)(30−5)
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A movie theatre rewards its loyal customers by offering them discounts   [#permalink] 18 Jul 2019, 04:53

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