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
OA C
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BTGmoderatorDC
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Original ratio:BTGmoderatorDC 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
A new recipe calls for a doubling of the ratio of flour to water.
Doubling F/W = 7/4, we get:
2 * 7/4 = 7/2
Resulting ratio:
F:W:S = 7:2:1
A halving of the ratio of flour to sugar.
Halving F/S = 7/1, we get:
(1/2)(7/1) = 7/2
Resulting ratio:
F:W:S = 7:2:2
Since W:S = 2:2 = 1:1, the new recipe requires an equal amount of water and sugar.
If the new recipe calls for 8 cups of water, how much sugar is required?
sugar = water = 8 cups
The correct answer is C.
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BTGmoderatorDC 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
OA C
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.
Answer: C
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