If you used 10 cups of water, which mixture would use more salt? How much more? Explain or show your reasoning.

Here are recipes for two mixtures of salt and water that taste different. Mixture A: salt (teaspoons) water (cups) 4 5 7 8 3/4 9 11 1/4 Mixture B is defined by the equation y=2.5x , where x is the number of teaspoons of salt and y is the number of cups of water. Respond to the following questions: 1. If you used 10 cups of water, which mixture would use more salt? How much more? Explain or show your reasoning. 2. Which mixture tastes saltier? Explain how you know.

Mixture A: salt water

4 5

7 8 3/4

9 11 1/4

Water = 5 cups when salt = 4 teaspoons

5 = k * 4

k = 5/4

y = 5/4x

Mixture B is defined by the equation y=2.5x ,

Where,

y = number of cups of water.

x = number of teaspoons of salt

Mixture A:

y = 5/4x

Mixture B:

y = 2.5x

When y = 10 cups

Mixture A:

y = 5/4x

10 = 5/4x

x = 10 ÷ 5/4

= 10 × 4/5

= 40/5

x = 8

Mixture A salt = 8 teaspoons

Mixture B:

y = 2.5x

10 = 2.5x

x = 10 / 2.5

= 4

x = 4

Mixture B salt = 4 teaspoons

Mixture A use more salt

Mixture A uses 4 teaspoons more of salt than mixture B

Mixture A tastes saltier because it uses more teaspoons of salt for the same cups of water than mixture B