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

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.