Question

1. when rice is prepared, the amount of rice varies directly as the amount of water required. if 2 cups of rice requires 4.5 cups of water, what is the total number of cups of water needed to prepare 5 cups of rice?

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Explanation:

Step1: Define direct variation

Let $r$ = cups of rice, $w$ = cups of water. Direct variation: $r = kw$, where $k$ is constant.

Step2: Solve for constant $k$

Substitute $r=2$, $w=4.5$:
$2 = k \times 4.5$
$k = \frac{2}{4.5} = \frac{4}{9}$

Step3: Rewrite variation formula

$r = \frac{4}{9}w$, rearrange to solve for $w$:
$w = \frac{9}{4}r$

Step4: Calculate water for 5 cups rice

Substitute $r=5$:
$w = \frac{9}{4} \times 5 = \frac{45}{4} = 11.25$

Answer:

11.25