linear system: chemist has 25%, 50% acid solns; needs 200mL

[Liane]

A chemist has a 25% and a 50% acid solution. How much of each solution should be used to form 200 mL of a 35% solution. HELP, I can't set up the two equations. Thanks.

 

[Liane]

Re: Help with a linear system

ok, so is it

x + y = 200
.25x + .50y = .35(x + y)

 

[Mrspi]

Re: Help with a linear system

ok, so is it

x + y = 200
.25x + .50y = .35(x + y)

Looks great!!

Now, from the first equation, x + y = 200....so you could write your system this way:

x + y = 200
.25x + .50y = .35(200)

And, you could solve the first equation for either x or y...I'll solve for y:
x + y = 200
y = 200 - x

Substitute that in the second equation:

.25x + .50(200 - x) = .35(200)

Now you have an equation with just one variable. You should be able to solve that for x. And once you have the value of x, you can get y by using the equation y = 200 - x.

I hope this helps you.