Respuesta :
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.
