A pharmacy mixes different concentrations of saline solutions for its customers. The pharmacy has a supply of two concentrations, 0.4% and 4%. The function y equals StartFraction left parenthesis 100 right parenthesis left parenthesis 0.04 right parenthesis plus x left parenthesis 0.004 right parenthesis Over 100 plus x EndFraction
gives the concentration of the saline solution after adding x milliliters of the 0.4% solution to 100 milliliters of the 4% solution. How many milliliters of the 0.4% solution must be added to the 4% solution to get a 0.85% solution?
We want to find the value of x that makes y equal to 0.85%. So we have the equation:
0.85 = (100 * 0.04 + x * 0.004) / (100 + x)
Now we can solve for x. First, let's simplify the equation:
0.85 * (100 + x) = 100 * 0.04 + x * 0.004
85 + 0.85x = 4 + 0.004x
0.85x - 0.004x = 4 - 85
0.846x = -81
Now, divide both sides by 0.846 to solve for x:
x = -81 / 0.846 ≈ -95.73
We cannot have a negative amount of solution, so there is no solution in this context.