Jill wants to make 15 no of a 40% acid solution by mixing together a 30% acid solution and a 60% acid solution. how much of each solution must she use?

15 no?  Don't recognize "no."  I'll use "units" instead.

Let f represent the volume of the 40% acid solution.
Let t represent that of the 30% solution, and s that of the 60% solution.

Then s + t = 15 units.  Then, (15 units) - s = t

0.30t + 0.60s=(15 units)(0.40)
Mult. this by 100 to elim. fractions:    30t + 60s = 600

Subst (15 units - s) for t, 30 (15-s) + 60s = 600

                                         4500 - 30s + 60s = 600
                                                           30s     = 150
                                                               s = 5 units

Then t = (15 units - 5 units) = 10 units.

Use 10 units of the 30% solution and 5 units of the 60% solution.

Check:  Does (10)(.3) + (5)(.6) = (15)(.4)?  Yes