Question

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 1

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

Step-by-step 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

`x + y = 2` ...[1]

Percentage of the final salt solution = 35%

`x* 50\%+y* 25\%=2 gal* 35\%`

`50x+25y=70`

`10x+5y=14`....[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.