Nia and Trey both had a sore throat so their mom told them to gargle with warm salt water. Nia mixed 1 teaspoon salt with 3 cups of water.
Trey mixed 12 teaspoon salt with 112 cups of water.

Nia tasted Trey’s salt water. She said,

“I added more salt so I expected that mine would be more salty, but they
taste the same.”

Explain why the salt water mixtures taste the same.

  both mixes used the same ratio of salt to water.

Step-by-step explanation:

Nia used double Trey's recipe, doubling both the salt and the water. So, the ratio of salt to water was the same in each mix.

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Trey's recipe: (1/2 tsp salt : 1.5 cups water)

Nia's recipe: 2(1/2 tsp salt : 1.5 cups water) = 1 tsp salt : 3 cups water

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2