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Ezra pays $0.75 each time he takes a public transport to reach his sch

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Ezra pays $0.75 each time he takes a public transport to reach his sch  [#permalink]

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New post 01 Oct 2019, 21:05
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A
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C
D
E

Difficulty:

  45% (medium)

Question Stats:

55% (02:19) correct 45% (02:22) wrong based on 47 sessions

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Competition Mode Question



Ezra pays $0.75 each time he takes a public transport to reach his school. Students who frequently use this service may instead purchase token each month for $13 and then pay $0.30 per each ride. If Ezra need to take the bus twice a day for K days next month and will not use the bus on any other day, what is the least possible value of K for which Ezra will save money by using the token?

(A) 10
(B) 12
(C) 15
(D) 18
(E) 28

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Re: Ezra pays $0.75 each time he takes a public transport to reach his sch  [#permalink]

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New post 01 Oct 2019, 22:41
1
Cost of ride per trip of bus ride without monthly pass=$0.75
Cost of ride per trip after paying $13 monthly pass =$0.3
We are to determine the minimum number of days, k, that Ezra has to take the bus using a token in order to make a saving.

0.75*2k > 13 + 0.3*2k
1.5k - 0.6k >13
0.9k>13
k>14.444
The minimum possible number of days for Ezra to make a saving using the bus pass has to be 15.

The answer is therefore C.
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Re: Ezra pays $0.75 each time he takes a public transport to reach his sch  [#permalink]

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New post 01 Oct 2019, 23:25
1
Since Ezra takes bus twice a day total money spent without the token for travel f ‘k’ days = 0.75*2*k
If token is taken then total money spent for travel ‘k’ days = 13 + 0.3*2*k

Now as per question to save money while using token

0.75*2*k > 13 + 0.3*2*k
1.5k – 0.6k > 13 [k > 0]
0.9k > 13
k > 14.4

Answer (C).
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Re: Ezra pays $0.75 each time he takes a public transport to reach his sch  [#permalink]

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New post 01 Oct 2019, 23:36
1
0.75*2*k > 13 + 0.60k

Or, 1.50 k > 13 + 0.60k

Or, 0.90k > 13

Or, k > 14

Among the given option only (C) fits in , Answer must be (C)
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Re: Ezra pays $0.75 each time he takes a public transport to reach his sch  [#permalink]

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New post 01 Oct 2019, 23:50
1
Current plan expense per day ; 0.75*2 ; 1.5$*k
Another plan ; 13+0.3*2 ; 13+0.6*k

using answer options we can find when saving money will start

K----CP------NP(13$)
10----15-----19
12----18-----20.2
15---22.5----22 ; YES she starts to save 0.5$ per trip
IMO C ; 15 is sufficient


Ezra pays $0.75 each time he takes a public transport to reach his school. Students who frequently use this service may instead purchase token each month for $13 and then pay $0.30 per each ride. If Ezra need to take the bus twice a day for K days next month and will not use the bus on any other day, what is the least possible value of K for which Ezra will save money by using the token?

(A) 10
(B) 12
(C) 15
(D) 18
(E) 28
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Re: Ezra pays $0.75 each time he takes a public transport to reach his sch  [#permalink]

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New post 02 Oct 2019, 05:46
1
Quote:
Ezra pays $0.75 each time he takes a public transport to reach his school. Students who frequently use this service may instead purchase token each month for $13 and then pay $0.30 per each ride. If Ezra need to take the bus twice a day for K days next month and will not use the bus on any other day, what is the least possible value of K for which Ezra will save money by using the token?

(A) 10
(B) 12
(C) 15
(D) 18
(E) 28


current cost - token cost > 0
0.75*2*k - (13+0.3*2*k) > 0
1.5k - 13 - 0.6k > 0
0.9k > 13
k > 14… = 15 days

Answer (C)
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Re: Ezra pays $0.75 each time he takes a public transport to reach his sch  [#permalink]

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New post 02 Oct 2019, 06:36
$0.75 * 2 =$1.5 per day
—> If Ezra has a token ($13 for a month) for the next month, she will spend $0.6 per day for K days.

In order to save money,
—>13+ 0.6K must be less than 1.5K

13+0.6K< 1.5K
0.9K> 13
K> 130/9= 14.4
K>14.4
—> the least possible value of K is 15
The answer is C

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Re: Ezra pays $0.75 each time he takes a public transport to reach his sch  [#permalink]

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New post 05 Oct 2019, 16:57
Bunuel wrote:

Competition Mode Question



Ezra pays $0.75 each time he takes a public transport to reach his school. Students who frequently use this service may instead purchase token each month for $13 and then pay $0.30 per each ride. If Ezra need to take the bus twice a day for K days next month and will not use the bus on any other day, what is the least possible value of K for which Ezra will save money by using the token?

(A) 10
(B) 12
(C) 15
(D) 18
(E) 28


We can create the following inequality:

0.75(2K) > 13 + 0.3(2K)

1.5K > 13 + 0.6K
0.9K > 13

K > 14.4

Answer: C
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Re: Ezra pays $0.75 each time he takes a public transport to reach his sch  [#permalink]

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New post 23 Oct 2019, 17:36
Quote:
Ezra pays $0.75 each time he takes a public transport to reach his school. Students who frequently use this service may instead purchase token each month for $13 and then pay $0.30 per each ride. If Ezra need to take the bus twice a day for K days next month and will not use the bus on any other day, what is the least possible value of K for which Ezra will save money by using the token?

(A) 10
(B) 12
(C) 15
(D) 18
(E) 28


You can look at the difference:
Cost each day without pass = 1.5$
Cost each day with pass = 0.6$

The difference is 0.9$.

Now we need to recover the cost of 13$. So in 14 days we would have recovered 12.6$. So on the 15th day we will profit from the ownership of the pass.

Hence C.
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Re: Ezra pays $0.75 each time he takes a public transport to reach his sch   [#permalink] 23 Oct 2019, 17:36
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