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12. To prepare an aquarium for use, you can clean it with a saltwater solution. The amount of salt varies directly with the volume of the water. The solution has 2 teaspoons of aquarium salt for every gallon of water. a. How many teaspoons of aquarium salt are needed for 5 gallons of water? b. Write an equation that relates x gallons of water to y teaspoons of salt. c. Use the equation to find the number of gallons of water to use for 12 teaspoons of salt.

Sagot :

Given:

The solution has 2 teaspoons of aquarium salt for every gallon of water.

a.) How many teaspoons of aquarium salt are needed for 5 gallons of water?

- To be able to determine how many teaspoons of aquarium salt are needed, we will be using ratios and proportions.

[tex]\text{ 2 teaspoon of salt : 1 gallon of water = x : 5 gallons of water}[/tex]

Where,

x = teaspoons of aquarium salt

We get,

[tex]\text{ 2 teaspoon of salt : 1 gallon of water = x : 5 gallons of water}[/tex][tex]\frac{2}{1}\text{ = }\frac{x}{5}[/tex][tex]\text{ (2)(5) = (x)(1)}[/tex][tex]\text{ 10 = x}[/tex]

Therefore, you will be needing 10 teaspoons of aquarium salt for 5 gallons of water.

b.) Write an equation that relates x gallons of water to y teaspoons of salt.

Let,

x = gallons of water

y = teaspoons of salt

[tex]\text{ }\frac{2\text{ teaspoons of salt}}{1\text{ gallon}}\text{ = }\frac{y}{x}\text{ }\rightarrow\text{ }\frac{2}{1}\text{ = }\frac{y}{x}\text{ }\rightarrow\text{ 2 = }\frac{y}{x}[/tex][tex]\text{ 2x = y}[/tex]

Therefore, the equation of the mixture will be 2x = y.

c.) Use the equation to find the number of gallons of water to use for 12 teaspoons of salt.​ Substitute, y = 12.

[tex]\text{ 2x = y}[/tex][tex]\text{ 2x = 12}[/tex][tex]\text{ }\frac{2x}{2}\text{ = }\frac{12}{2}[/tex][tex]\text{ x = 6}[/tex]

Therefore, you will be needing 6 gallons of water for 12 teaspoons of salt.

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