High School

Mariam uses 4 tablespoons of sugar to make 2 cups of lemonade, while Michelle puts 7 tablespoons of sugar into 4 cups of lemonade. Whose lemonade will be sweeter?

Answer :

To determine whose lemonade will be sweeter, we need to compare the ratios of sugar to lemonade for both Mariam and Michelle.

Let's set up the ratios for each person:

  1. Mariam: 4 tablespoons of sugar / 2 cups of lemonade
  2. Michelle: 7 tablespoons of sugar / 4 cups of lemonade

First, we simplify each ratio:

  1. Mariam's ratio:
    [tex]\frac{4}{2} = 2 ext{ tablespoons of sugar per cup of lemonade}[/tex]

  2. Michelle's ratio:
    [tex]\frac{7}{4} ext{ tablespoons of sugar per cup of lemonade}[/tex]

Next, we compare the two simplified ratios to see whose is larger:

  • Mariam: 2 tablespoons of sugar per cup of lemonade
  • Michelle: 1.75 tablespoons of sugar per cup of lemonade

Comparing these values, 2 is greater than 1.75. Therefore, Mariam's lemonade will be sweeter than Michelle's.

In conclusion, Mariam's lemonade will be sweeter because it has a higher ratio of sugar to lemonade.

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