In a certain coffee shop, the ratio of orders for coffee, tea, and wat

Question

In a certain coffee shop, the ratio of orders for coffee, tea, and water is 5:6:10. In the afternoon, the ratio of orders for coffee to tea tripled and the ratio of orders for coffee to water halved. What is the minimum number of coffee orders that could have been made in the afternoon ?

A. 1
B. 2
C. 4
D. 5
E. 6

A. 1
B. 2
C. 4
D. 5
E. 6

stne · Accepted Answer

C:T:W  = 5:6:20

In afternoon , C:T  = 15:6  and C:W  =5:20

Equating coffee we have, C:W  = 15:60

Final ratio  15:6:60

Since all numbers need to be integers we can reduce by  3  to get  5:2:20

Minimum Coffee  = 5

Ans D

Hope it's clear

onlymalapink · Answer

does anyone have a better answer' I dont get it.

Posted from my mobile device

sushantkotecha · Answer

Original ratio for coffee : tea : water is 5 : 6 : 10

In the Afternoon,

i) ratio for coffee : tea triples

\frac{5}{6}  x 3 = \frac{15}{6}

ii) ratio for coffee : water halves

\frac{5}{10}  x  \frac{1}{2}  =  \frac{5}{20}

now, the ratio for coffee : tea : water is 15 : 6 : 60

if we simplify the ratio by dividing everything by 3, we get 5 : 2 : 20
therefore, the minimum number of coffee orders that could have been made in the afternoon is 5.
Answer D

hope this is helpful

onlymalapink · Answer

basically i cant wrap my head around 60 for water

sushantkotecha · Answer

we have two different ratios which include coffee: 15:6 and 5:20, so to combine all of them into a single ratio, we have to make coffee equal in both the ratios.

we have 2 options, to either simplify the first ratio from 15:6 (dividing by 3) to 5:2 or match the second ratio of 5:20 (multiplying by 3) to get 15:60 where coffee will be same in both the ratios.

i have used the second method which gives me 15:6:60 and then i simplify it by dividing with its HCF.

see that first method directly gives us the answer without the need of further simplifying the ratio - 5:2:20.

hope this is helpful

onlymalapink · Answer

Thanks, That makes a whole lot of sense when you mention it.

Posted from my mobile device

SergejK · Answer

Also, as T does not have a multiple of 5, the final answer, the minimum servings of coffee, must be a multiple of 5. Only if we can reduce all three components of a ratio by 5, can it be a different answer. As T never changes, easy to see that the answer must be 5.

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In a certain coffee shop, the ratio of orders for coffee, tea, and wat

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In a certain coffee shop, the ratio of orders for coffee, tea, and wat

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