SOLUTION: How much pure water must be mixed with 3 pints of 70% developer to produce a misture that is 13% developer?

Question 150518: How much pure water must be mixed with 3 pints of 70% developer to produce a misture that is 13% developer?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
How much pure water must be mixed with 3 pints of 70% developer to produce a
mixture that is 13% developer?
.
He started with:
3 pints of 70% developer
That means the amount of developer in the solution is:
.70 * 3 = 2.1 pints
.
Let x = amount of water added
then
2.1/(x+3) = .13(x+3)
2.1 = .13(x+3)^2
16.154 = (x+3)^2
16.154 = x^2 + 6x + 9
0 = x^2 + 6x - 7.154
.
Since you can't factor, you must apply the quadratic equation.
Doing so, produces two solutions one positive and one negative. We can throw out the negative solution cause it doesn't make sense. Therefore, the positive answer must be our solution:
x = 1.02 pints
.
Below is the solution of the quadratic equation:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=64.616 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 1.01920390127199, -7.01920390127199. Here's your graph:

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