Question

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.

Answer 1

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

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}: 1/3=(1)/(3)\\\\\text{Water}:3/3=1\\`

Thus 1 : 3 is equivalent to the ratio
`(1)/(3):1`, which means that Nia's solution has
`(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
`(1)/(2):1(1)/(2)` in Trey’s solution.

On dividing the amount of salt and the amount of water by
`1(1)/(2)`, the ratio will be the same.

`\text{salt}:(1)/(2)/ 1(1)/(2)=(1)/(3)\\\\\text{Water}:1(1)/(2)/1(1)/(2)=1`

So Trey’s ratio is also equal to the ratio
`(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.