Tanvi and her friend Beth are making cookies for their school's cookie swap. Tanvi mixes 1 cup of chocolate chips and 3 cups of plain sugar cookie dough in a small bowl. Beth mixes 2 cups of chocolate chips and 6 cups of plain sugar cookie dough in a larger bowl. Once the cookies are baked, the girls are ready for a chocolaty snack. Whose batch of cookies was more chocolaty?

Question

GPT-4o mini · Answer

To determine whose batch of cookies was more chocolaty, we need to compare the ratio of chocolate chips to dough in each batch.

Tanvi's batch:

Chocolate chips: 1 cup
Plain sugar cookie dough: 3 cups

The total amount of dough in Tanvi's batch is therefore: 1 cup (chocolate chips) + 3 cups (dough) = 4 cups

Now, we can find the ratio of chocolate chips to the total dough: \[ \text{Ratio for Tanvi} = \frac{1 \text{ cup of chocolate chips}}{4 \text{ cups total}} = \frac{1}{4} \]

Beth's batch:

Chocolate chips: 2 cups
Plain sugar cookie dough: 6 cups

The total amount of dough in Beth's batch is: 2 cups (chocolate chips) + 6 cups (dough) = 8 cups

Now, we can find the ratio of chocolate chips to the total dough: \[ \text{Ratio for Beth} = \frac{2 \text{ cups of chocolate chips}}{8 \text{ cups total}} = \frac{2}{8} = \frac{1}{4} \]

Conclusion: Both Tanvi and Beth have the same ratio of chocolate chips to dough, which is \(\frac{1}{4}\). Therefore, neither batch of cookies is more chocolaty; they are equally chocolaty.