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# Bon-Bean, a coffee shop, served a total of 460 cups of coffee and tea

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Math Expert
Joined: 02 Sep 2009
Posts: 59588
Bon-Bean, a coffee shop, served a total of 460 cups of coffee and tea  [#permalink]

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02 Oct 2016, 05:56
00:00

Difficulty:

55% (hard)

Question Stats:

68% (02:38) correct 32% (02:21) wrong based on 87 sessions

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Bon-Bean, a coffee shop, served a total of 460 cups of coffee and tea yesterday. 270 of these cups contained caffeine, and the number of decaffeinated tea cups was twice the total number of tea cups that contained caffeine. If Bon-Bean served 250 coffee cups yesterday, how many of them were decaffeinated?

A. 50
B. 70
C. 140
D. 190
E. 210

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Re: Bon-Bean, a coffee shop, served a total of 460 cups of coffee and tea  [#permalink]

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02 Oct 2016, 06:25
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Bunuel wrote:
Bon-Bean, a coffee shop, served a total of 460 cups of coffee and tea yesterday. 270 of these cups contained caffeine, and the number of decaffeinated tea cups was twice the total number of tea cups that contained caffeine. If Bon-Bean served 250 coffee cups yesterday, how many of them were decaffeinated?

A. 50
B. 70
C. 140
D. 190
E. 210

Tc : Tea caffeine
Td : Tea No caffeine
Cc : Coffee Caffeine
Cd : Coffee No Caffeine

As per question, Tc + Td + Cc + Cd = 460 -- (1)

Also, Tc + Cc = 270 -- (2)

Td = 2 * Tc -- (3)

Cc + Cd = 250 -- (4)

Now, substituting (4) in (1), we will have Tc + Td + 250 = 460

or Tc + Td = 210. -- (5)

Substitute (3) in (5), we will get Tc = 70. Substitute Tc in (2), we will get Cc = 200

Now substitute Cc in (4), we will get Cd = 50. hence, A
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Re: Bon-Bean, a coffee shop, served a total of 460 cups of coffee and tea  [#permalink]

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22 Nov 2019, 10:32
Bunuel wrote:
Bon-Bean, a coffee shop, served a total of 460 cups of coffee and tea yesterday. 270 of these cups contained caffeine, and the number of decaffeinated tea cups was twice the total number of tea cups that contained caffeine. If Bon-Bean served 250 coffee cups yesterday, how many of them were decaffeinated?

A. 50
B. 70
C. 140
D. 190
E. 210

Please find the solution below:
Attachments

20191122_224655[1].jpg [ 1.3 MiB | Viewed 228 times ]

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Re: Bon-Bean, a coffee shop, served a total of 460 cups of coffee and tea   [#permalink] 22 Nov 2019, 10:32
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# Bon-Bean, a coffee shop, served a total of 460 cups of coffee and tea

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