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Twenty gallons of a salt solution consists of 35% salt. It is the result of mixing a 50% solution with a 25% solution. How many gallons of each of the solutions was used? Let x= the number of gallons of the 50% solution and y= the number of gallons of the 25% solution. The corresponding modeling system is?

Answer :

Answer:

The volume of the 50% solution used is 0.8 gallons and the volume of 25% solution used is 1.2 gallons.

Explanation:

Let the volume of the 50% solution be be x gallons.

Let the volume of 25% solution be y gallons.

Total volume of the solution after mixing above volumes of the solutions = 2 gallons

x gal + y gal = 2 gal

[tex]x + y = 2[/tex] ...[1]

Percentage of the final salt solution = 35%

[tex]x\times 50\%+y\times 25\%=2 gal\times 35\%[/tex]

[tex]50x+25y=70[/tex]

[tex]10x+5y=14[/tex]....[2]

On solving [1] and [2] , we get:

x = 0.8 , y = 1.2

So, the volume of the 50% solution used is 0.8 gallons and the volume of 25% solution used is 1.2 gallons.

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