SOLUTION: a scientist has 35% acid solution and 20% acid solution and she needs 3 liters of 25% acid solution write a linear equation and how much of each solution she should use

Question 708588: a scientist has 35% acid solution and 20% acid solution and she needs 3 liters of 25% acid solution write a linear equation and how much of each solution she should use
Found 2 solutions by aaronwiz, josgarithmetic:
Answer by aaronwiz(69) (Show Source): You can put this solution on YOUR website!
.35x+.2y=.25
x+y=3
solve this system using a method of your choice
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
This question requires TWO linear equations because it asks for the results for TWO variables.

Begin with a rational equation which will essentially be a linear equation with two variables.

The scientist has a lower concentration acid and a higher concentration acid. subsript 1 is for the low, and subscript 2 is for the high. The target concentration can use a subscript, t. Let these three variables (not unknown) be , , and .
Let a and b be the volume of the low and high concentration acid solutions to use. We also know the volume of the target acid solution this scientist wants to make, call it V.

We have this rational equation:

We will also need to use .

So we have two equations and two unknown variables. Continue with multiplying both sides of the rational equation by V. From there, you are free to use substitution method, elimination method, or some simple matrix operations to solve the system.
Solve this system for a and b:

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