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# A recipe requires 2 1/2 cups of flour 2 3/4 cups of sugar

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A recipe requires 2 1/2 cups of flour 2 3/4 cups of sugar  [#permalink]

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Updated on: 17 May 2013, 17:23
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13
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Difficulty:

55% (hard)

Question Stats:

65% (02:24) correct 35% (02:43) wrong based on 300 sessions

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A recipe requires 2 1/2 (mixed number) cups of flour 2 3/4 (mixed number) cups of sugar and 1 1/3 (mixed number) cups of milk to make one cake. Victor has 15 cups if flour, 16 cups of sugar and 8 cups of milk. What is the greatest number of cakes Victor can make using this recipe?

A. 5
B. 6
C. 7
D. 8
E. 9

Originally posted by clciotola on 17 May 2013, 08:03.
Last edited by Bunuel on 17 May 2013, 17:23, edited 1 time in total.
Renamed the topic and edited the question.
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Updated on: 17 May 2013, 08:11
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Easiest would be just crosscheck 1 by 1,
like, first check for flour, he has 15 cups, i.e. 15/2.5 = 6 cups can be made.
then come to sugar, sugar per cup (if he wants to make 6 cups of recipe) = 16/6 = 2+2/3 (what he has), but he need 2+3/4; so not available.
So, ans =5

Originally posted by mkdureja on 17 May 2013, 08:10.
Last edited by mkdureja on 17 May 2013, 08:11, edited 1 time in total.
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17 May 2013, 08:10
1
clciotola wrote:
Hi All,

any way to approch this kind of question very fast, please explain step by step if you can

A receipe requires 2 1/2 (mixed number) cups of flour 2 3/4(mixed number) cups of sugar and 1 1/3(mixed number) cups of milk to make one cake.
Victor has 15 cups if flour, 16 cups of sugar and 8 cups of milk.
What is the gretest number of cakes Victor can make using this recipe?

a 5
b 6
c 7
d 8
e 9

The answer would be [A]. The idea is to pick out that ingredient which produces the minimal value when divided.

Among the fractions:
Flour = 5/2
Sugar = 11/4
and finally Milk = 4/3.

I normally start with the terms with the lowest values and divide them to find the number of cakes possible. But Its actually safe to calculate them all, since it barely takes a min. Sugar leads to 16*4/11 which can be approximated to an integer as 5. For all the other ingredients the value is 6. Hence the minimal number would be taken into consideration!

Hope it helps!

Regards,
Arpan
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17 May 2013, 08:13
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2
clciotola wrote:
Hi All,

any way to approch this kind of question very fast, please explain step by step if you can

A receipe requires 2 1/2 (mixed number) cups of flour 2 3/4(mixed number) cups of sugar and 1 1/3(mixed number) cups of milk to make one cake.
Victor has 15 cups if flour, 16 cups of sugar and 8 cups of milk.
What is the gretest number of cakes Victor can make using this recipe?

a 5
b 6
c 7
d 8
e 9

Hi clciotola, you can do this kind of question with more work up front or less work up front. I'd do it with less work up front so let's go through that method:

Less work up front: Go through each item and see what the greatest number of cakes you can make with each. The lowest of these will be the right answer.

Flour: 15 cups, we need 2.5 cups each. Just keep going up the line to see how many cakes we can make: That means I can make 2 cakes with 5 cups, so 6 cakes overall with 15 cups. I've already got the answer narrowed to either A or B.

Sugar: 16 cups, we need 2.75 cups each. Same principle. I can make 2 cups with 5.5 cups, so to make 6 cakes I'd need 16.5 cups. I don't have that much sugar, so we're limited to 5 cakes. No need to even do milk because we're already at 5. Sugar will be the limiting factor.

You can also do this by figuring out which item will be the limiting factor. Since you have halfes, quarters and thirds, you'll need to put them on common bases by multiplying by 12. This will be ugly and I don't recommend it, although it will eventually work out to the same answer.

Hope this helps!
-Ron
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17 May 2013, 08:19
clciotola wrote:
Hi All,

any way to approch this kind of question very fast, please explain step by step if you can

A receipe requires 2 1/2 (mixed number) cups of flour 2 3/4(mixed number) cups of sugar and 1 1/3(mixed number) cups of milk to make one cake.
Victor has 15 cups if flour, 16 cups of sugar and 8 cups of milk.
What is the gretest number of cakes Victor can make using this recipe?

a 5
b 6
c 7
d 8
e 9

Given ratio of the ingredients = $$\frac{5}{2}:\frac{11}{4}:\frac{4}{3}$$ --> Multiply by 6 = 15:16.5:8 Thus, for making 6 cakes, we need 16.5 cups of sugar, however as we have only 16, the no of cakes we can make is only 5.
A.
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Re: A recipe requires 2 1/2 cups of flour 2 3/4 cups of sugar  [#permalink]

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19 May 2013, 05:19
clciotola wrote:
A recipe requires 2 1/2 (mixed number) cups of flour 2 3/4 (mixed number) cups of sugar and 1 1/3 (mixed number) cups of milk to make one cake. Victor has 15 cups if flour, 16 cups of sugar and 8 cups of milk. What is the greatest number of cakes Victor can make using this recipe?

A. 5
B. 6
C. 7
D. 8
E. 9

Similar questions to practice:
m07-72458.html

Hope it helps.
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Re: A recipe requires 2 1/2 cups of flour 2 3/4 cups of sugar  [#permalink]

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26 Jan 2014, 20:15
A recipe requires 2 1/2 (mixed number) cups of flour 2 3/4 (mixed number) cups of sugar and 1 1/3 (mixed number) cups of milk to make one cake. Victor has 15 cups if flour, 16 cups of sugar and 8 cups of milk. What is the greatest number of cakes Victor can make using this recipe?

-----------------

You will be limited by the ingredient that can bake the lowest number of cakes.

Flour: 15 / 5/2 = 6 cakes
Sugar: 16 / 11/4 = 5 cakes (round down since can't partial cake is equivalent to no cake)
Milk: 8 / 4/3 = 6 cakes

Limited by sugar. Can only bake 5 cakes.
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Re: A recipe requires 2 1/2 cups of flour 2 3/4 cups of sugar  [#permalink]

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07 Nov 2016, 13:56

If we know the amount available to us and the amount required, we will be able to figure out the answer based on whichever input we have the least of. That will significantly limit what we can do with the other two inputs.

(1) We have 5/2 (or 2.5 cups) of flour available to us --> 15/(5/2) = 6 recipes worth of flour
(2) 11/4 cups of sugar --> 16/(11/4) = 5 recipes worth of sugar

We don't need to go beyond this point because we already have 5 as an answer choice.
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Re: A recipe requires 2 1/2 cups of flour 2 3/4 cups of sugar  [#permalink]

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06 Mar 2019, 05:55
So the ratios are f:s:m = 5/2 : 11/4 : 4/3

If you convert the information we're given into the respective fractions, we have 30/2 , 64/4 and 24/3.

Now it's all a matter of calculating how much of each ingredient "goes" into each cake.

So 30/5 = 6 possible cakes
64/11 = 5 possible cakes (remainder)
24/4 = 6 possible cakes

So we have the necessary amount of flour and milk for 6 cakes, but only enough sugar for 5, so answer is 5 cakes.
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Re: A recipe requires 2 1/2 cups of flour 2 3/4 cups of sugar   [#permalink] 06 Mar 2019, 05:55
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