Ascientist has two solutions which she has labeled solution a and solution b. each contains salt. she knows that solution a is 55% salt and solution b is 85% salt. she wants to obtain 30 ounces of mixture that is 60% salt. how many ounces of each solution should she use?

Let x be the amount of oz in solution A, then solution of A = .55x
The amount of a is known(x), to find the amount of B, we have to take into consideration the last info: ...to obtain 30 oz of a 60& mixture.
So we know that A + B at the will generate a solution at 60%.
So if the amount of A = x then the amount of B =30-x
0.55x + 0.85(30-x) = (30)(0.6)
0.55x+25.5 - 0.85x = 18 ===>  -0.30x = 18-25.5 ==> -0.3x = -7.5
0.30x = 7.5 ==> x = 25 oz
Then it will have 25 oz at 55% & 5oz at 85%