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Finger [1]
3 years ago
12

Nia and Trey both had sore throats, so their mom told them to gargle with warm salt water. Nia mixed 1 teaspoon salt with 3 cups

warm water. Trey mixes 1 /2 teaspoon salt with one and 1/2 cups warm water. Nia tasted Trey’s water and said, “I added more salt, so I expected that mine would be more salty, but they taste the same! Explain why both salt water mixtures taste the same.
Mathematics
1 answer:
Harrizon [31]3 years ago
4 0

Answer:

Each mixture has the same amount of salt for every 1 cup of water.

Step-by-step explanation:

It is provided that:

  • Nia mixed 1 teaspoon salt with 3 cups warm water.
  • Trey mixes 1 /2 teaspoon salt with one and 1/2 cups warm water.

The ratio of the number of teaspoons of salt to the number of cups of water is 1 : 3 in Nia's solution.

On dividing the amount of salt and the amount of water by 3, the ratio will be the same.

\text{Salt}: 1\div3=\frac{1}{3}\\\\\text{Water}:3\div3=1\\

Thus 1 : 3 is equivalent to the ratio \frac{1}{3}:1, which means that Nia's solution has \frac{1}{3}teaspoon of salt for every cup of water.

The ratio of the number of teaspoons of salt to the number of cups of water is \frac{1}{2}:1\frac{1}{2} in Trey’s solution.

On dividing the amount of salt and the amount of water by 1\frac{1}{2}, the ratio will be the same.

\text{salt}:\frac{1}{2}\div 1\frac{1}{2}=\frac{1}{3}\\\\\text{Water}:1\frac{1}{2}\div1\frac{1}{2}=1

So Trey’s ratio is also equal to the ratio \frac{1}{3}:1.

Since each mixture has the same amount of salt for every 1 cup of water, they are equally salty and taste the same.

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