A recipe calls for 6 cups of water and 4 cups of flour.
a. If the recipe is increased to use 6 cups of flour, how much flour should be used? Example.
b. If the recipe is decreased to 2 cups of water, how much flour should be used? Example.
water/flour = 6/4 = 3/2.
a. 3/2 = W/6.
2W = 18,
W = 9 cups of water.
b. 3/2 = 2/F.
3F = 4,
F = 4/3 = 1 1/3 cups of flour.
a. 6 cups, naturally!
b. 2 is 1/3 of 6, so use 1/3 of 4 cups of flour.
To solve both parts of the question, we can use proportionality to find the amount of flour needed based on the amount of water used in the recipe.
a. If the recipe is increased to use 6 cups of flour, we can set up a proportion to find the amount of flour needed.
Let's call the unknown amount of flour needed when 6 cups of flour are used as 'x'. The proportion can be set up as:
6 cups of water / 4 cups of flour = 2 cups of water / x (unknown amount of flour)
To solve for x, we can cross-multiply and solve for it:
6x = 4 * 2
6x = 8
x = 8 / 6
x = 4/3
x ≈ 1.33 cups of flour
Therefore, if the recipe is increased to use 6 cups of flour, approximately 1.33 cups of flour should be used.
b. If the recipe is decreased to 2 cups of water, we can use the same method to find the amount of flour needed.
Let's call the unknown amount of flour needed when 2 cups of water are used as 'y'. The proportion can be set up as:
2 cups of water / y (unknown amount of flour) = 6 cups of water / 4 cups of flour
Again, we can cross-multiply and solve for y:
2 * 4 = 6y
8 = 6y
y = 8 / 6
y = 4 / 3
y ≈ 1.33 cups of flour
Therefore, if the recipe is decreased to 2 cups of water, approximately 1.33 cups of flour should be used.