To find the unit rate for Recipe A in terms of tablespoons of chocolate powder per 1 cup of milk, you need to determine what you can divide \( \frac{4}{3} \) cups of milk by to get 1 cup of milk.
To convert \( \frac{4}{3} \) cups to 1 cup, you can divide by \( \frac{4}{3} \) (because \( \frac{4}{3} \) divided by \( \frac{4}{3} \) is 1).
Now you need to do the same with the number of tablespoons of chocolate powder. You have 2 tablespoons of chocolate powder for \( \frac{4}{3} \) cups of milk. To find the amount of chocolate powder per 1 cup, you can calculate it as follows:
- Divide the amount of chocolate powder (2 tablespoons) by the same value you used to convert the milk (which is \( \frac{4}{3} \)):
\[ \text{Amount of chocolate per cup} = \frac{2 \text{ tablespoons}}{\frac{4}{3} \text{ cups}} = 2 \text{ tablespoons} \times \frac{3}{4} = \frac{6}{4} = \frac{3}{2} \text{ tablespoons} \]
So, for Recipe A, there are \( \frac{3}{2} \) tablespoons of chocolate powder per 1 cup of milk.
Next, let’s find the unit rate for Recipe B.
For Recipe B, it calls for 3 tablespoons of chocolate powder for \( \frac{6}{5} \) cups of milk. To find the amount of chocolate powder per 1 cup of milk, you follow the same logic:
- Divide the amount of chocolate powder (3 tablespoons) by \( \frac{6}{5} \):
\[ \text{Amount of chocolate per cup} = \frac{3 \text{ tablespoons}}{\frac{6}{5} \text{ cups}} = 3 \text{ tablespoons} \times \frac{5}{6} = \frac{15}{6} = \frac{5}{2} \text{ tablespoons} \]
So, for Recipe B, there are \( \frac{5}{2} \) tablespoons of chocolate powder per 1 cup of milk.
Now we can compare the two recipes:
- Recipe A: \( \frac{3}{2} \) tablespoons per cup of milk
- Recipe B: \( \frac{5}{2} \) tablespoons per cup of milk
Since \( \frac{5}{2} \) (or 2.5) is greater than \( \frac{3}{2} \) (or 1.5), Recipe B tastes more chocolatey.
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