Questions: Which of the following two recipes given below will create a juice that will taste more "orangey"? Use ratio tables to explain. Recipe A: 2 cups of orange concentrate to 3 cups of water Recipe B: 6 cups of orange concentrate to 7 cups of water Choose the correct answer below. A. Recipe A uses less water so it will taste more "orangey." B. When both recipes use 12 cups of concentrate, recipe A uses less water, so it will taste more "orangey." C. When both recipes use 12 cups of concentrate, recipe B uses less water, so it will taste more "orangey." D. Recipe B uses more concentrate so it will taste more "orangey."

Which of the following two recipes given below will create a juice that will taste more "orangey"? Use ratio tables to explain.
Recipe A: 2 cups of orange concentrate to 3 cups of water
Recipe B: 6 cups of orange concentrate to 7 cups of water

Choose the correct answer below.
A. Recipe A uses less water so it will taste more "orangey."
B. When both recipes use 12 cups of concentrate, recipe A uses less water, so it will taste more "orangey."
C. When both recipes use 12 cups of concentrate, recipe B uses less water, so it will taste more "orangey."
D. Recipe B uses more concentrate so it will taste more "orangey."

Transcript text: Which of the following two recipes given below will create a juice that will taste more "orangey"? Use ratio tables to explain. Recipe A: 2 cups of orange concentrate to 3 cups of water Recipe B: 6 cups of orange concentrate to 7 cups of water Choose the correct answer below. A. Recipe A uses less water so it will taste more "orangey." B. When both recipes use 12 cups of concentrate, recipe $A$ uses less water, so it will taste more "orangey." C. When both recipes use 12 cups of concentrate, recipe B uses less water, so it will taste more "orangey." D. Recipe B uses more concentrate so it will taste more "orangey."

Solution

Solution Steps

Step 1: Calculate the Ratios for Each Recipe

For Recipe A, the amount of orange concentrate is $2$ cups and the amount of water is $3$ cups. The total amount of liquid is: \[ \text{Total}_A = 2 + 3 = 5 \text{ cups} \] The ratio of orange concentrate to total liquid for Recipe A is: \[ \text{Ratio}_A = \frac{2}{5} = 0.4 \]

For Recipe B, the amount of orange concentrate is $6$ cups and the amount of water is $7$ cups. The total amount of liquid is: \[ \text{Total}_B = 6 + 7 = 13 \text{ cups} \] The ratio of orange concentrate to total liquid for Recipe B is: \[ \text{Ratio}_B = \frac{6}{13} \approx 0.4615 \]

Step 2: Compare the Ratios

Now we compare the two ratios: \[ \text{Ratio}_A = 0.4 \quad \text{and} \quad \text{Ratio}_B \approx 0.4615 \] Since $0.4615 > 0.4$, Recipe B has a higher ratio of orange concentrate to total liquid.