Liz and Larry are arguing over who makes better chocolate chip cookies. Liz likes to use 3 cups of brown sugar for every 8 cups of flour. Larry prefers to use 2 cups of brown sugar for every 5 cups of flour. Do Liz and Larry use the same ratio of brown sugar to flour?
Question
Liz and Larry are arguing over who makes better chocolate chip cookies. Liz likes to use 3 cups of brown sugar for every 8 cups of flour. Larry prefers to use 2 cups of brown sugar for every 5 cups of flour. Do Liz and Larry use the same ratio of brown sugar to flour?
Solution
To determine if Liz and Larry use the same ratio of brown sugar to flour, we need to compare their ratios.
Step 1: Identify the ratios. Liz's ratio of brown sugar to flour is 3:8. Larry's ratio of brown sugar to flour is 2:5.
Step 2: Convert the ratios to the same scale. To do this, we can convert each ratio to a unit ratio (the amount of brown sugar per 1 cup of flour).
For Liz: Divide the amount of brown sugar (3 cups) by the amount of flour (8 cups). 3 ÷ 8 = 0.375 cups of brown sugar per cup of flour.
For Larry: Divide the amount of brown sugar (2 cups) by the amount of flour (5 cups). 2 ÷ 5 = 0.4 cups of brown sugar per cup of flour.
Step 3: Compare the unit ratios. Liz uses 0.375 cups of brown sugar per cup of flour, while Larry uses 0.4 cups of brown sugar per cup of flour.
So, Liz and Larry do not use the same ratio of brown sugar to flour. Larry uses slightly more brown sugar per cup of flour than Liz does.
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