Amanda and her brother, Brian, are making chocolate milk. Amanda mixes 1 ounce of chocolate syrup and 6 ounces of milk in her cup. Brian mixes 2 ounces of chocolate syrup and 10 ounces of milk in his cup. Whose milk is more chocolaty?

Answer 1

To determine whose chocolate milk is more chocolaty, we can calculate the ratio of chocolate syrup to the total volume of the mixture for both Amanda and Brian.

Amanda's mixture:

• Chocolate syrup: 1 ounce
• Milk: 6 ounces
• Total mixture: 1 ounce + 6 ounces = 7 ounces

The ratio of chocolate syrup to total mixture for Amanda is: \[ \text{Ratio for Amanda} = \frac{\text{Chocolate syrup}}{\text{Total mixture}} = \frac{1}{7} \]

Brian's mixture:

• Chocolate syrup: 2 ounces
• Milk: 10 ounces
• Total mixture: 2 ounces + 10 ounces = 12 ounces

The ratio of chocolate syrup to total mixture for Brian is: \[ \text{Ratio for Brian} = \frac{\text{Chocolate syrup}}{\text{Total mixture}} = \frac{2}{12} = \frac{1}{6} \]

Now, we can compare the two ratios:

• Amanda's ratio: \( \frac{1}{7} \)
• Brian's ratio: \( \frac{1}{6} \)

To compare \( \frac{1}{7} \) and \( \frac{1}{6} \), we note that: \[ \frac{1}{6} > \frac{1}{7} \]

Therefore, since \( \frac{1}{6} \) is larger than \( \frac{1}{7} \), Brian's chocolate milk is more chocolaty than Amanda's chocolate milk.