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A movie theatre rewards its loyal customers by offering them discounts

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

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New post 17 Jul 2019, 06:59
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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. \(225 × 10 + (40 + 5)(40 - 5)\)


 

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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, 07:18
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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?

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: 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. John watched 95 movies in this movie theatre last year.

Asked: The dollar amount that he paid for the tickets of the 95 movies is equivalent to which of the following?

For first 10 movies, ticket price is $50/movie => Total ticket price for 10 movies = $500
For next 10 movies, ticket price is $45/movie => Total ticket price for next 10 movies = $450
For next 10 movies, ticket price is $40/movie => Total ticket price for next 10 movies = $400
For next 10 movies, ticket price is $35/movie => Total ticket price for next 10 movies = $350
For next 10 movies, ticket price is $30/movie => Total ticket price for next 10 movies = $300
For next 10 movies, ticket price is $25/movie => Total ticket price for next 10 movies = $250
For all other movies, ticket price is $25/movie => Total ticket price for next x movies = $25x

He watched 95 = 10 + 10 + 10 + 10 + 10 + 10 + 35 movies
Total ticket price = $ ( 500+450+400+350+300+250+25*35)
= 50(5+6+7+8+9+10) + (30-5)*(30+5)
= 45*50 + (30-5)*(30+5)
= 225*10 + (30-5)*(30+5)

IMO 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, 08:23
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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:
movies.PNG
movies.PNG [ 27.46 KiB | Viewed 384 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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Re: A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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New post 17 Jul 2019, 08:34
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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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Re: A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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New post 17 Jul 2019, 11:59
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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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Re: A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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New post 17 Jul 2019, 20:14
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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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Re: A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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New post 18 Jul 2019, 02:42
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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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Re: A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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New post 18 Jul 2019, 02:54
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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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A movie theatre rewards its loyal customers by offering them discounts  [#permalink]

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New post 18 Jul 2019, 03:53
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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, 03:53

A movie theatre rewards its loyal customers by offering them discounts

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