Emily made blueberry muffins for her scout troop's bake sale. For her first batch, she used 1 cup of blueberries and 2 cups of oats. She didn't think that would make enough muffins, so she made a larger second batch with 3 cups of blueberries and 6 cups of oats. When she took the last tray out of the oven, her little brother asked if he could have a muffin with lots of blueberries as a snack. Which batch had a greater ratio of blueberries to oats?

Answer 1

To determine which batch had a greater ratio of blueberries to oats, we need to calculate the ratio of blueberries to oats for each batch.

For the first batch:

• Blueberries: 1 cup
• Oats: 2 cups
• Ratio of blueberries to oats = \( \frac{\text{blueberries}}{\text{oats}} = \frac{1}{2} \)

For the second batch:

• Blueberries: 3 cups
• Oats: 6 cups
• Ratio of blueberries to oats = \( \frac{\text{blueberries}}{\text{oats}} = \frac{3}{6} = \frac{1}{2} \)

Now we compare the ratios:

• First batch ratio = \( \frac{1}{2} \)
• Second batch ratio = \( \frac{1}{2} \)

Both batches have the same ratio of blueberries to oats, which is \( \frac{1}{2} \). Therefore, neither batch has a greater ratio of blueberries to oats; they are equal.