Emily made blueberry muffins for her scout group'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?
Question
Emily made blueberry muffins for her scout group'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?
Solution
The ratio of blueberries to oats for the first batch is 1:2 and for the second batch is 3:6.
To compare these ratios, we need to simplify them to their lowest terms.
The first ratio simplifies to 1:2 (since 1 and 2 have no common factors other than 1).
The second ratio simplifies to 1:2 as well (since 3 and 6 can both be divided by 3).
Therefore, both batches have the same ratio of blueberries to oats. Neither batch has a greater ratio of blueberries to oats.
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