The ratio of flour to water to sugar in a recipe is 7:4:1. The ration in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and halving of the 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

How do you sole this problem correctly?

We start with

F : W : S at 7 : 4 : 1

so, F:W is 7:4 and F:S is 7:1

if we double the F:W ratio we'd go to 14:4 or 7:2 ... in either case
there is double the amount of F to W that we had originally.

if we halve the F:S ratio, we'd go to 7:2 or 3.5 : 1 or 14:4 in any case
there is half the amount of F to S that we had originally.

The new F:W:S ratio is 14:4:4

If the recipe calls for 8 cups of water, we'd need 8 cups of sugar
(since we need 4 cups of sugar for every 4 cups of water)

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