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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?

Answer 1

To determine if Liz and Larry use the same ratio of brown sugar to flour, we need to calculate the ratio of brown sugar to flour for both of them.

For Liz:

• Brown sugar: 3 cups
• Flour: 8 cups

The ratio of brown sugar to flour for Liz is: \[ \text{Ratio}_\text{Liz} = \frac{3}{8} \]

For Larry:

• Brown sugar: 2 cups
• Flour: 5 cups

The ratio of brown sugar to flour for Larry is: \[ \text{Ratio}_\text{Larry} = \frac{2}{5} \]

Now, we need to compare the two ratios \(\frac{3}{8}\) and \(\frac{2}{5}\). To do this, we can cross-multiply:

• Cross-multiplying yields: \[ 3 \times 5 = 15 \] \[ 2 \times 8 = 16 \]

Since \(15 \neq 16\), the ratios are not equivalent. Therefore, Liz and Larry do not use the same ratio of brown sugar to flour.