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Last year, a coffee roasting company purchased new roasting machines

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Bunuel
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Last year, a coffee roasting company purchased new roasting machines [#permalink] New post   19 May 2019, 21:43
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Last year, a coffee roasting company purchased new roasting machines to bring their total number of machines to 10. These 10 machines can roast 210 lbs of coffee beans in 3 hours. Before purchasing the new machines, the company could roast 84 lbs of beans in 2 hours. If all of the machines work at the same constant rate, how many machines did the company buy last year?

A. 1
B. 2
C. 3
D. 4
E. 5
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D
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Rakesh1987
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Last year, a coffee roasting company purchased new roasting machines [#permalink] New post   Updated on: 20 May 2019, 02:45
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Bunuel wrote:
Last year, a coffee roasting company purchased new roasting machines to bring their total number of machines to 10. These 10 machines can roast 210 lbs of coffee beans in 3 hours. Before purchasing the new machines, the company could roast 84 lbs of beans in 2 hours. If all of the machines work at the same constant rate, how many machines did the company buy last year?

A. 1
B. 2
C. 3
D. 4
E. 5


Roasting capacity of each machine in pounds/ hour= \(\frac{210}{10*3} = 7\)
Before buying machines, company could roast 42 lbs (\(\frac{84}{2}\)) each hour, therefore it had \(\frac{42}{7} = 6\) machines.
New machines bought= 10- 6 =4. Answer is D.

Please hit +1 Kudos if you liked the explanation.

Originally posted by Rakesh1987 on 19 May 2019, 22:38.
Last edited by Rakesh1987 on 20 May 2019, 02:45, edited 2 times in total.
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Re: Last year, a coffee roasting company purchased new roasting machines [#permalink] New post   20 May 2019, 02:27
Bunuel wrote:
Last year, a coffee roasting company purchased new roasting machines to bring their total number of machines to 10. These 10 machines can roast 210 lbs of coffee beans in 3 hours. Before purchasing the new machines, the company could roast 84 lbs of beans in 2 hours. If all of the machines work at the same constant rate, how many machines did the company buy last year?

A. 1
B. 2
C. 3
D. 4
E. 5


rate per machine ; 210/3*10 ; 7lbs per hour
so in 2 hrs ; 14 lbs per hr
84lbs can be made by 84/14; 6 machines
new machines purchased; 10-6 ; 4
IMO D
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Re: Last year, a coffee roasting company purchased new roasting machines [#permalink] New post   17 Jan 2024, 07:52
Bunuel wrote:
Last year, a coffee roasting company purchased new roasting machines to bring their total number of machines to 10. These 10 machines can roast 210 lbs of coffee beans in 3 hours. Before purchasing the new machines, the company could roast 84 lbs of beans in 2 hours. If all of the machines work at the same constant rate, how many machines did the company buy last year?

A. 1
B. 2
C. 3
D. 4
E. 5

Solving in parts -
Quote:
These 10 machines can roast 210 lbs of coffee beans in 3 hours.


10 machines can roast 70 lbs of coffee beans in 1 hours

1 machines can roast 7 lbs of coffee beans in 1 hours

Quote:
Before purchasing the new machines, the company could roast 84 lbs of beans in 2 hours.


We know \(7*m*2 = 84\)

Or, \(m = 6\)

Thus, originally the firm had 6 machines and it increased to 10 , so 4 machines were purchased during the year, Answer must be (D)
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Re: Last year, a coffee roasting company purchased new roasting machines [#permalink]
17 Jan 2024, 07:52
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