Joseph needs 6 1/2 cups of cooked rice for a recipe of Nasi Goreng. If 2 cups of uncooked rice with 2 1/2 cups of water make 4 1/3 cups of cooked rice, how many cups of uncooked rice does Joseph need for his recipe ? How much water should he add?
To find out how many cups of uncooked rice Joseph needs for his recipe, we can use a proportion to relate the amounts of cooked and uncooked rice.
Let's analyze the given information:
2 cups of uncooked rice + 2 1/2 cups of water make 4 1/3 cups of cooked rice.
We need to convert all the measurements to fractions:
2 cups of uncooked rice = 2 cups
2 1/2 cups of water = 2 1/2 cups
4 1/3 cups of cooked rice = 4 1/3 cups
Now, let's set up the proportion:
2 cups of uncooked rice / 4 1/3 cups of cooked rice = x cups of uncooked rice / 6 1/2 cups of cooked rice
To solve for x (the unknown amount of uncooked rice), we can cross-multiply:
(2 cups * 6 1/2 cups of cooked rice) = (4 1/3 cups * x cups of uncooked rice)
Multiplying the fractions:
(13/2) * (13/3) = (4 1/3) * x
Multiplying the numerators and denominators:
(13 * 13) / (2 * 3) = (13/3) * x
(169) / (6) = (13/3) * x
Now, let's solve for x by dividing both sides of the equation by (13/3):
(169/6) / (13/3) = x
To simplify, we invert and multiply the fraction on the right side of the equation:
(169/6) * (3/13) = x
Multiplying the numerators and denominators:
(169 * 3) / (6 * 13) = x
507 / 78 = x
So, Joseph needs approximately 6.5 cups of uncooked rice for his recipe.
To find out how much water he should add, we can use the same proportion:
2 cups of uncooked rice / 2 1/2 cups of water = 6 1/2 cups of cooked rice / y cups of water
To solve for y, we can cross-multiply:
(2 cups * y cups of water) = (2 1/2 cups * 6 1/2 cups of cooked rice)
Multiplying the fractions:
(2/1) * (13/2) = (13/2) * y
Multiplying the numerators and denominators:
(2 * 13) / 1 = (13/2) * y
26 / 1 = (13/2) * y
Next, we solve for y by dividing both sides of the equation by (13/2):
(26/1) / (13/2) = y
To simplify, we invert and multiply the fraction on the right side of the equation:
(26/1) * (2/13) = y
Multiplying the numerators and denominators:
(26 * 2) / (1 * 13) = y
52 / 13 = y
So, Joseph should add approximately 4 cups of water for his recipe.
2/(4 1/3) = x/6.5
Solve for x.