Recipe A calls for 2 tablespoons of chocolate powder for every

Question

4
3
​
of a cup of milk. Recipe B calls for 3 tablespoons of chocolate powder for every
6
5
​
of a cup of milk. Which chocolate milk recipe tastes more chocolatey?
To finish finding the amount of chocolate powder you would need for 1 cup of milk in Recipe A, rename
3
8
​
as a mixed number.
÷
4
3
​

÷
4
3
​

Recipe A
Milk (cups) Chocolate Powder (tablespoons)
4
3
​
2
1 ?
2÷
4
3
​

= 2·
3
4
​

=
2·4
1·3
=
3
8
​

=

Answer 1

To determine which recipe tastes more chocolatey, we need to compare the ratio of chocolate powder to milk for both recipes and then complete the calculations for Recipe A.

Recipe A:

• Chocolate Powder: 2 tablespoons
• Milk: \( \frac{4}{3} \) cups

To find out how much chocolate powder is needed for 1 cup of milk in Recipe A, we set up the ratio:

1. Set up the ratio of chocolate powder to milk: \[ \text{Ratio (chocolate powder per cup)} = \frac{2 \text{ tablespoons}}{\frac{4}{3} \text{ cups}} \]

2. To divide by a fraction, multiply by its reciprocal: \[ \frac{2}{\frac{4}{3}} = 2 \cdot \frac{3}{4} = \frac{6}{4} = \frac{3}{2} \]

So, Recipe A requires \( \frac{3}{2} \) tablespoons of chocolate powder for every 1 cup of milk.

Recipe B:

• Chocolate Powder: 3 tablespoons
• Milk: \( \frac{6}{5} \) cups

To find out how much chocolate powder is needed for 1 cup of milk in Recipe B, we set up the ratio:

1. Set up the ratio of chocolate powder to milk: \[ \text{Ratio (chocolate powder per cup)} = \frac{3 \text{ tablespoons}}{\frac{6}{5} \text{ cups}} \]

2. To divide by a fraction, multiply by its reciprocal: \[ \frac{3}{\frac{6}{5}} = 3 \cdot \frac{5}{6} = \frac{15}{6} = \frac{5}{2} \]

So, Recipe B requires \( \frac{5}{2} \) tablespoons of chocolate powder for every 1 cup of milk.

Comparison:

• Recipe A: \( \frac{3}{2} \) tablespoons for 1 cup of milk = 1.5 tablespoons per cup
• Recipe B: \( \frac{5}{2} \) tablespoons for 1 cup of milk = 2.5 tablespoons per cup

Conclusion:

Recipe B has more chocolate powder per cup of milk than Recipe A. Therefore, Recipe B tastes more chocolatey.