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."
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:
TotalA=2+3=5 cups
The ratio of orange concentrate to total liquid for Recipe A is:
RatioA=52=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:
TotalB=6+7=13 cups
The ratio of orange concentrate to total liquid for Recipe B is:
RatioB=136≈0.4615
Step 2: Compare the Ratios
Now we compare the two ratios:
RatioA=0.4andRatioB≈0.4615
Since 0.4615>0.4, Recipe B has a higher ratio of orange concentrate to total liquid.
Final Answer
The recipe that will taste more "orangey" is Recipe B. Thus, the answer is \\(\boxed{D}\\).