Math Fraction Problem

Question

I am at the moment in the $5$th chapter of IGCSE mathematics and currently need help for this problem. Joseph needs $6\frac12$ cups of cooked rice for a recipe of nasi goreng. If $2$ cups of uncooked rice with $2 \frac12$ cups of water make $4 \frac13$ cups of cooked rice, How many cups of uncooked rice does Joseph need for his recipe? How much water should he add?

Answer 1

As a hint, I can see a couple of equations that would help you get started.

Let $u$ represent the amount of uncooked rice, let $c$ represent the amount of cooked rice, and let $w$ represent the amount of water. All of these amounts are measured in cups.

The given recipe states that $2$ cups of uncooked rice with $2\frac12$ cups of water yields $4\frac13$ cups of cooked rice. We must assume that uncooked rice and water should be scaled in tandem. For example, we could double the recipe, and our inputs would be $4$ cups of uncooked rice and $5$ cups of water.

We can even make an equation out of that: $4u=5w$.

Another equation relates the amount of uncooked rice to the amount of cooked rice. Note that $4\frac13=\frac{13}{3}$, so the equation would be $2u=\frac{13}{3}c$.

What should you scale that equation by so you wind up with the needed amount of cooked rice? What does that tell you about the amount of water?