Kathy and Omar are planning a party to honor the teachers at their school. They each suggest a recipe for apple cider punch to serve at the party.
Kathy’s Recipe
13 over 4 parts apple cider
31 fourth parts ginger ale
Omar’s Recipe
31 half parts apple cider
21 half parts ginger ale
For each recipe, write a unit rate to represent the parts of apple cider per part of ginger ale. Then, determine which recipe will have the stronger apple taste. Explain how you determined your answer.
Kathy: (13/4) / (31/4) = 13/31
Omar: (31/2) / (21/2) = 31/21
clearly, 31/21 > 13/31
To find the unit rates for each recipe, we need to divide the parts of apple cider by the parts of ginger ale.
Kathy's Recipe:
Parts of apple cider: 13/4
Parts of ginger ale: 31/4
Unit rate for Kathy's Recipe: (13/4) / (31/4) = 13/31
Omar's Recipe:
Parts of apple cider: 31/2
Parts of ginger ale: 21/2
Unit rate for Omar's Recipe: (31/2) / (21/2) = 31/21
To determine which recipe will have the stronger apple taste, we need to compare the unit rates. The larger the unit rate, the stronger the apple taste.
Comparing the unit rates:
Kathy's Recipe: 13/31
Omar's Recipe: 31/21
Since 31/21 is larger than 13/31, it means that Omar's Recipe will have the stronger apple taste.
To find the unit rate, we need to determine how many parts of apple cider are there per part of ginger ale in each recipe.
For Kathy's recipe:
- Apple cider: 13/4 parts
- Ginger ale: 31/4 parts
Let's simplify these fractions:
- Apple cider: 3.25 parts
- Ginger ale: 7.75 parts
Therefore, the unit rate for Kathy's recipe is 3.25 parts of apple cider per 7.75 parts of ginger ale.
For Omar's recipe:
- Apple cider: 31/2 parts
- Ginger ale: 21/2 parts
Let's simplify these fractions:
- Apple cider: 15.5 parts
- Ginger ale: 10.5 parts
Therefore, the unit rate for Omar's recipe is 15.5 parts of apple cider per 10.5 parts of ginger ale.
To determine which recipe will have the stronger apple taste, we need to compare the unit rates. The lower the unit rate, the stronger the apple taste will be.
Comparing the unit rates:
- Kathy's recipe: 3.25 parts of apple cider per 7.75 parts of ginger ale
- Omar's recipe: 15.5 parts of apple cider per 10.5 parts of ginger ale
Based on the unit rates, Kathy's recipe has a lower unit rate, indicating a stronger apple taste. Therefore, Kathy's recipe will have a stronger apple taste compared to Omar's recipe.
Well, let's calculate the unit rates for both recipes.
For Kathy's recipe, the unit rate would be 13/4 parts of apple cider per 31/4 parts of ginger ale. Simplifying, we get 3.25 parts of apple cider per part of ginger ale.
For Omar's recipe, the unit rate would be 31/2 parts of apple cider per 21/2 parts of ginger ale. Simplifying, we get 15.5 parts of apple cider per part of ginger ale.
Now, to determine which recipe will have a stronger apple taste, we need to consider the ratio of apple cider to ginger ale. The higher the ratio of apple cider, the stronger the apple taste.
Comparing the unit rates, we can see that Omar's recipe has a higher ratio of apple cider to ginger ale (15.5:1) compared to Kathy's recipe (3.25:1). So, Omar's recipe will have a stronger apple taste.
But hey, let's not forget that taste is subjective! Some people might prefer a stronger apple taste, while others might prefer a milder one. In the end, it's all about personal preference!