We can start solving the problem by using a system of equations. Let's call the number of ounces of solution a x and the number of ounces of solution b y. From the problem statement, we know that:
x + y = 150 (because the total amount of the mixture is 150 ounces)
0.6x + 0.9y = 0.65(x + y) (because the mixture is 65% salt, and we can find the amount of salt in the mixture by multiplying the percentage by the total amount)
We can use the first equation to solve for one of the variables in terms of the other:
y = 150 - x
Now we can substitute this expression for y into the second equation:
0.6x + 0.9(150 - x) = 0.65(150)
0.6x + 135 - 0.9x = 97.5
-0.3x = -37.5
x = 125
Now we can use the first equation to find the value of y:
y = 150 - x
y = 150 - 125
y = 25
So the scientist should use 125 ounces of solution a and 25 ounces of solution b to obtain 150 ounces of a mixture that is 65% salt.