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# The ratio of flour to water to sugar in a recipe is 7:4:1.

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Joined: 11 Oct 2013
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The ratio of flour to water to sugar in a recipe is 7:4:1.  [#permalink]

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21 Jan 2014, 15:10
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Question Stats:

65% (01:58) correct 35% (02:13) wrong based on 411 sessions

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The ratio of flour to water to sugar in a recipe is 7:4:1. The ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar. If the new recipe calls for 8 cups of water, how much sugar is required?

(A) 4 cups
(B) 6 cups
(C) 8 cups
(D) 12 cups
(E) 16 cups

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Re: The ratio of flour to water to sugar in a recipe is 7:4:1.  [#permalink]

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21 Jan 2014, 21:38
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3111987 wrote:
The ratio of flour to water to sugar in a recipe is 7:4:1. The ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar. If the new recipe calls for 8 cups of water, how much sugar is required?

(A) 4 cups
(B) 6 cups
(C) 8 cups
(D) 12 cups
(E) 16 cups

Flour:Water:Sugar = 7:4:1

Flour:Water = 7:4
New Ratio of Flour:Water = 14:4 = 7:2 (Multiplying the ratio by 2)

Flour:Sugar = 7:1
New Ratio of Flour:Sugar = 7:2 (Halving the ratio)

New Ratio of Flour:Water:Sugar = 7:2:2

For every 2 cups of water, there is 2 cups of sugar. IF you have 8 cups of water, you need 8 cups of sugar.
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Re: The ratio of flour to water to sugar in a recipe is 7:4:1.  [#permalink]

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22 Jan 2014, 16:29
VeritasPrepKarishma wrote:
3111987 wrote:
The ratio of flour to water to sugar in a recipe is 7:4:1. The ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar. If the new recipe calls for 8 cups of water, how much sugar is required?

(A) 4 cups
(B) 6 cups
(C) 8 cups
(D) 12 cups
(E) 16 cups

Flour:Water:Sugar = 7:4:1

Flour:Water = 7:4
New Ratio of Flour:Water = 14:4 = 7:2 (Multiplying the ratio by 2)

Flour:Sugar = 7:1
New Ratio of Flour:Sugar = 7:2 (Halving the ratio)

New Ratio of Flour:Water:Sugar = 7:2:2

For every 2 cups of water, there is 2 cups of sugar. IF you have 8 cups of water, you need 8 cups of sugar.

dear Karishma big thanks for explanation)
questioin:
why when you doubling the ratio you multiply both and 7 and 4 but when you halving you apply to one side of ratio 7:2???
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Re: The ratio of flour to water to sugar in a recipe is 7:4:1.  [#permalink]

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23 Jan 2014, 00:01
3111987 wrote:
The ratio of flour to water to sugar in a recipe is 7:4:1. The ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar. If the new recipe calls for 8 cups of water, how much sugar is required?

(A) 4 cups
(B) 6 cups
(C) 8 cups
(D) 12 cups
(E) 16 cups

Hello,

Flour/Water = 7/4, Flour/Sugar = 7/1

Double the ratio of Flour/Water = 7/4 * 2 = 7/2

Halve the ratio of Flour to Sugar = 7 * 1/2 = 7/2

The new ratio of Flour: Water: Sugar = 7:2:2

For 8 cups of water in the new recipe, sugar required will be 8 cups.

Hope this helps
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Re: The ratio of flour to water to sugar in a recipe is 7:4:1.  [#permalink]

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23 Jan 2014, 03:06
2
3111987 wrote:
VeritasPrepKarishma wrote:
3111987 wrote:
The ratio of flour to water to sugar in a recipe is 7:4:1. The ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar. If the new recipe calls for 8 cups of water, how much sugar is required?

(A) 4 cups
(B) 6 cups
(C) 8 cups
(D) 12 cups
(E) 16 cups

Flour:Water:Sugar = 7:4:1

Flour:Water = 7:4
New Ratio of Flour:Water = 14:4 = 7:2 (Multiplying the ratio by 2)

Flour:Sugar = 7:1
New Ratio of Flour:Sugar = 7:2 (Halving the ratio)

New Ratio of Flour:Water:Sugar = 7:2:2

For every 2 cups of water, there is 2 cups of sugar. IF you have 8 cups of water, you need 8 cups of sugar.

dear Karishma big thanks for explanation)
questioin:
why when you doubling the ratio you multiply both and 7 and 4 but when you halving you apply to one side of ratio 7:2???

I am not sure I follow you.

Original Ratio of Flour:Water $$= 7:4 = \frac{7}{4}$$
New Ratio of Flour:Water (original will be doubled) $$= \frac{7}{4}*2 = \frac{14}{4}$$

Thereafter, I brought 14/4 to lowest terms 7/2.

Original Ratio of Flour:Sugar $$= 7:1 = \frac{7}{1}$$
New Ratio of Flour:Sugar (original will be halved) $$= \frac{7}{1*2} = \frac{7}{2}$$
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Re: The ratio of flour to water to sugar in a recipe is 7:4:1.  [#permalink]

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25 Jun 2017, 08:24

Flour: Water:Sugar = 7:4:1

F:W is doubled so it becomes 14:4
And F:S is halved so it becomes 7:2 or 14:4

Thus new ratio is F:W:S = 14:4:4 or 7:2:2

That is, the ratio of water and sugar is same. So if there are 8 cups of water there should be 8 cups of sugar!
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The ratio of flour to water to sugar in a recipe is 7:4:1.  [#permalink]

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16 Jan 2018, 13:43
Initial:
Flour(F):Water(W):Sugar(S)=7:4:1
Now, let's separate the ratios for convenience.
F:W=7:4 ; F:S=7:1
Now, bring both ratios to the same denominator by multiplying,
F:W=7:4 ; F:S=28:4
Now, quantity of F in F:W is doubled,
F:W=14:4
Now, quantity of F in F:S is halved,
F:S=14:4

Since the denominators are equal, we can write the new ratio together as,
F:W:S=14:4:4

We see that water and sugar are both in equal quantities in the ratio. Hence, if we add 8 cups of water, we have to add 8 cups of sugar too.
ANS. C
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Re: The ratio of flour to water to sugar in a recipe is 7:4:1.  [#permalink]

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06 Feb 2019, 11:16
3111987 wrote:
The ratio of flour to water to sugar in a recipe is 7:4:1. The ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar. If the new recipe calls for 8 cups of water, how much sugar is required?

(A) 4 cups
(B) 6 cups
(C) 8 cups
(D) 12 cups
(E) 16 cups

F:W:S = 7:4:1

F/W = 14/4(doubling ) W/F = 4/14

F/S = 7/2(halving )(multiply both numerator and denominator by 2)

F/S = 14/4

Tally the ratios W:F:S = 4:14:4

So multiply the above ratio by 2

how much sugar is required => 8 cups
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Re: The ratio of flour to water to sugar in a recipe is 7:4:1.  [#permalink]

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06 Jul 2019, 18:05
3111987 wrote:
The ratio of flour to water to sugar in a recipe is 7:4:1. The ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar. If the new recipe calls for 8 cups of water, how much sugar is required?

(A) 4 cups
(B) 6 cups
(C) 8 cups
(D) 12 cups
(E) 16 cups

The original ratio is F : W : S = 7 : 4 : 1

Doubling the flour to water ratio gives us F: W = 14 : 4 = 7 : 2.

Halving the flour to sugar ratio gives us F : S = 3.5 : 1 = 7 : 2.

In the new recipe (or ratio), we see that water and sugar must be the same amount. Therefore, if the new recipe calls for 8 cups of water, we also need 8 cups of sugar.

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Re: The ratio of flour to water to sugar in a recipe is 7:4:1.   [#permalink] 06 Jul 2019, 18:05
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