Question

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1. connecting to real life you mix 0.25 cup of juice concentrate for every 2 cups of water to make 18 cups of juice.

how much juice concentrate do you use?
□ cups of juice concentrate
how much water do you use?
□ cups of water

Explanation:

Step1: Define the ratio

The ratio of juice concentrate to water is $0.25:2$. Let $c$ = cups of concentrate, $w$ = cups of water. Total juice: $c + w = 18$.

Step2: Simplify the ratio

Simplify $\frac{c}{w} = \frac{0.25}{2} = \frac{1}{8}$, so $w = 8c$.

Step3: Substitute into total equation

Substitute $w=8c$ into $c+w=18$:
$c + 8c = 18$
$9c = 18$

Step4: Solve for concentrate

$c = \frac{18}{9} = 2$

Step5: Solve for water

$w = 18 - c = 18 - 2 = 16$

Answer:

2 cups of juice concentrate
16 cups of water