Question

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 ?

Answer 1

To find the amount of uncooked rice Joseph needs, set up a proportion: (2 cups uncooked rice)/(4 1/3 cups cooked rice) = (x cups uncooked rice)/(6 1/2 cups cooked rice). Simplify the proportion to find x = 4 cups. To find the amount of water Joseph should add, use the same proportion and find that he should add 2 cups of water.

Step-by-step explanation:

To find the amount of uncooked rice Joseph needs for his recipe, we can set up a proportion using the information provided:

2 cups uncooked rice + 2 1/2 cups water = 4 1/3 cups cooked rice

Let x be the amount of uncooked rice Joseph needs.

We can set up the proportion:

(2 cups uncooked rice)/(4 1/3 cups cooked rice) = (x cups uncooked rice)/(6 1/2 cups cooked rice)

Simplifying the proportion, we get:

(2/4 1/3) = (x/6 1/2)

Converting the mixed numbers to improper fractions:

(2/4 + 1/3) = (x/6 + 1/2)

Using the LCD of 12:

(6/12 + 4/12) = (x/12 + 6/12)

Combining like terms:

(10/12) = (x/12 + 6/12)

Subtracting 6/12 from both sides:

(10/12) - (6/12) = (x/12)

Simplifying the left side:

(4/12) = (x/12)

Dividing both sides by 1/12:

(4/12) ÷ (1/12) = (x/12) ÷ (1/12)

Canceling out the common factor of 1/12:

4 = x

Therefore, Joseph needs 4 cups of uncooked rice for his recipe.

To find the amount of water Joseph should add, we can use the same proportion:

(2 cups uncooked rice)/(2 1/2 cups water) = (4 1/3 cups cooked rice)/(x cups water)

Simplifying the proportion, we get:

(2/2 1/2) = (4 1/3/x)

Converting the mixed numbers to improper fractions:

(2/(5/2)) = (13/3/x)

Using the reciprocal to solve for x:

(2/(5/2)) × (3/13) = (13/3/x) × (3/13)

Canceling out the common factors:

(2/1) = (1/x)

Therefore, Joseph should add 2 cups of water to the recipe.