Algebra word problems.

[HallsofIvy]

You don't say what kind if "chart" you mean so I am not going to say anything about a "chart".'

You want to determine how much of a 30% solution and how much of a 90% solution must be combined. That is, you want to determine two quantities and will need two equations. Let x be the amount of 30% solution and let y be the amount of 90% solution, both in gallons.

x gallons of 30% solution contains .3x gallons of glycerin and .7x gallons of water.
y gallons of 90% solution contains .9y gallons of glycerin and .1y gallons of water.

You want 100 gallons of a 75% solution so you want 75 gallons of glycerin and 25 gallons of water.

So .3x+ .9y= 75 and .7x+ .1y= 25.

Solve those two equations for x and y.

[Guest]

What happened to the question this was answering?

[sueambrose121]

I think you helped a lot here.

[Guest]

Since this has been here a while:
"So .3x+ .9y= 75 and .7x+ .1y= 25."

I would first multiply both equations by 10 to get
c3x+ 9y= 750 and 7x+ y= 250.

From the second equation, y= 250-7x. Replacing y in the first equation by that, 3x+ 9(250- 7x)= 3x+ 2250- 63x= 2250- 60x= 750. 60x= 2250- 750= 1500. x= 1500/60= 25.

y= 250- 7x= 250- 7(25)= 250- 175= 75.

You need to use 25 gallons of the 30% solution and 75 gallons of the 90% solution.

Check: 25 gallons+ 75 gallons= 100 gallons of solution.

25 gallons of 30% solution contains .3(25)= 7.5 gallons of glycerine. 75 gallons of 90% solution containes .9(75)= 67.5 gallons of glycerine for a total of 67.5+ 7.5= 75 gallons of glycerine. That is a 75/100= 75% solution as desired.