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John spent a total of $135 on baseball tickets. The price of a ticket

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Bunuel
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John spent a total of $135 on baseball tickets. The price of a ticket [#permalink] New post   24 Oct 2019, 00:17
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82% (01:09) correct 18% (00:49) wrong based on 34 sessions
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John spent a total of $135 on baseball tickets. The price of a ticket is either $12 for the field seats or $5 for the balcony. What is the minimum amount of dollars he could have spent for the $12 tickets?

A. $48
B. $60
C. $84
D. $96
E. $120
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B
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Re: John spent a total of $135 on baseball tickets. The price of a ticket [#permalink] New post   24 Oct 2019, 00:28
Let number of field seats be f
and number of balcony seats b

12f+5b=135
12f=135-5b
We can deduce that 12f must be a multiple of 5 (135-5b is a multiple of 5)

The lowest non-negative multiple of 5 is 0 --> 12*0=0 but we dont have 0 as an answer
The second is 5 itself --> 12*5=60

IMO
Ans: B

P.S In my modest opinion, in the stem there should be stated that at least one $12 ticket was bought
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Re: John spent a total of $135 on baseball tickets. The price of a ticket [#permalink] New post   24 Oct 2019, 00:44
Bunuel wrote:
John spent a total of $135 on baseball tickets. The price of a ticket is either $12 for the field seats or $5 for the balcony. What is the minimum amount of dollars he could have spent for the $12 tickets?

A. $48
B. $60
C. $84
D. $96
E. $120



Let he buy x number of 12 dollars tickets nd y number of 5 dollars ticket.

12x + 5y = 135

if x =0

12 *0 + 5y = 135

y = 27.

if x = 5

12 * 5 + 5*15 = 135.

Thus , minimum x = 5.

Total = 5*12 = 60.

B is the correct answer.
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Re: John spent a total of $135 on baseball tickets. The price of a ticket [#permalink] New post   31 Oct 2019, 04:09
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Solution



Given
    • John spent a total of $135 on baseball tickets
    • The price of a ticket is either $12 for the field seats or $5 for the balcony.

To find
    • The minimum amount of dollars he could have spent for the $12 tickets?

Approach and Working out
Let John took x tickets of field seats and y tickets of balcony then:
    • 12x + 5y = 135
    • Since we want y to be minimum, let us see if y can 0 then 1, or 2 and so on.
      o x =0 then 5y = 135
         for x =0, 12x =0
         However, it is not an option. So, question must have mentioned that john bought at least one ticket of each type.
      o 12x = 135 – 5y
         135 is a multiple of 5 and 5y is also a multiple of 5.
         So, 12 x also has to be a multiple of 5.
         12 is not a multiple of 5. So, x must be multiple of 5.
      o Hence, x = 0, 5, and so on.
      • However, x =0 does not give the answer.
      • X=5 or 12x = 60 should the least amount spent by Johnf or $ 12 tickets.

Thus, option B is the correct answer.

Correct Answer: Option B
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Re: John spent a total of $135 on baseball tickets. The price of a ticket [#permalink]
31 Oct 2019, 04:09
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