Ascientist wants a 66 ounce saline solution with concentration 12% . she has concentrations of 4% and 15% . how much of each solution must she use to get the desired concentration?

Let x and y represent the measure in ounces of the two given saline solutions.  We are mixing these two together, so x + y = 66 ounces.

The amount of the 4% solution to be used is 0.04x, and that of the 15% solution is 0.15y. 

This results in the equation .04x + 0.15y = 66(0.12).

Multiply both sides by 100 to remove the decimal fractions.  Then

4x + 15y = 66(12).  Now eliminate the variable x by recalling that x + y = 66 ounces, so that x = 66 - y.

Substituting, 4(66 - y) + 15y = 66(12)
Expanding, 264 - 4y + 15 y = 792
combining like terms:    11y = 528

Solving for y:  y = 528/11 = 48.  Then x = 66 - 48 = 18.

Use 48 ounces of the 15% solution and 18 ounces of the 4% solution to obtain 66 ounces of a 12% solution.