Question

Joseph needs 6 1/2 cups of cooked rice for a recipe of nasi gorang. 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 joshep need for this recipe? And how much water should be added?

Answer 1

The number of the cups of uncooked rice is 3 cups

The number of the cups of water is
`3(3)/(4)` cups

Explanation:

* Let us read the recipe of Nasi Gorang

- 2 cups of uncooked rice need
`2(1)/(2)` cups of water to

make
`4(1)/(3)` cups of cooked rice

- Joseph needs
`6(1)/(2)` cups of cooked rice

- We need to know how many cups of uncooked rice Joshep needs

for this recipe and how much water should be added

* We can solve this problem by using the ratio method

⇒ uncooked cups : water cups : cooked cups

⇒ 2 :
`2(1)/(2)` :
`4(1)/(3)`

⇒ x : y :
`6(1)/(2)`

- By using cross multiplication

∵ x (
`4(1)/(3)` ) = 2 (
`6(1)/(2)` )

∵
`4(1)/(3)` =
`(13)/(3)`

∵
`6(1)/(2)` =
`(13)/(2)`

∴ x (
`(13)/(3)` ) = 2 (
`(13)/(2)` )

∴
`(13)/(3)` x = 13

- Divide both sides by
`(13)/(3)`

∴ x = 3

∴ The number of the cups of uncooked rice is 3 cups

- By using cross multiplication

∵ y (
`4(1)/(3)` ) = (
`2(1)/(2)` )(
`6(1)/(2)` )

∵
`2(1)/(2)` =
`(5)/(2)`

∵
`6(1)/(2)` =
`(13)/(2)`

∵
`4(1)/(3)` =
`(13)/(3)`

∴
`(13)/(3)` y = (
`(5)/(2)` )(
`(13)/(2)` )

∴
`(13)/(3)` y =
`(65)/(4)`

- Divide both sides by
`(13)/(3)`

∴ y =
`3(3)/(4)`

∴ The number of the cups of water is
`3(3)/(4)` cups