To find the unit rate of rice per cup of veggies, we can start with the recipe's ratio of rice to veggies: 5 cups of rice for every 4 cups of veggies.
First, we can determine how much rice is needed for each cup of veggies:
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From the recipe ratio, we know:
- 4 cups of veggies corresponds to 5 cups of rice.
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To find the amount of rice needed for 1 cup of veggies, we can set up a proportion: \[ \frac{5 \text{ cups of rice}}{4 \text{ cups of veggies}} = \frac{x \text{ cups of rice}}{1 \text{ cup of veggies}} \]
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By cross-multiplying, we find: \[ 4x = 5 \]
\[ x = \frac{5}{4} \text{ cups of rice} \]
So, we find that for 1 cup of veggies, \( \frac{5}{4} \) cups of rice are needed.
Next, we can extend this to find out how much rice is needed for 20 cups of veggies:
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If 1 cup of veggies requires \( \frac{5}{4} \) cups of rice, then for 20 cups of veggies: \[ \text{Rice needed} = 20 \text{ cups of veggies} \times \frac{5}{4} \text{ cups of rice per cup of veggies} \]
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Calculating this gives: \[ = 20 \times \frac{5}{4} = \frac{100}{4} = 25 \text{ cups of rice} \]
In summary, the restaurant would need 25 cups of rice for 20 cups of veggies.
Here's a representation of your double number line:
Veggies (cups)
0 1 2 3 4
0 5. 10 15 20
Rice (cups)
0 5 10 15 20
- For 0 cups of veggies, you need 0 cups of rice.
- For 4 cups of veggies, you need 5 cups of rice.
- For 1 cup of veggies: \( \frac{5}{4} \) cups of rice.
- For 2 cups of veggies: \( 2.5 \) cups of rice.
- For 3 cups of veggies: \( 3.75 \) cups of rice.
- For 20 cups of veggies: 25 cups of rice.