A scientist has two kinds of solutions. The first solution is Solution A, which is an $80\%$ acid solution. The second solution is Solution B, which is a $30\%$ acid solution. (a) Find the amount of Solution A (in mL) that must be added to $500$ mL of Solution B in order to produce a $70\%$ acid solution. (b) Find the amount of Solution A and Solution B (in mL) that can be combined in order to form a $100$ mL solution that is $50\%$ acid. (c) Does there exist a combination of Solution A and Solution B that is $90\%$ acid?

Step-by-step explanation:

a ) Let the volume required be v .

v x .8 + 500 x .3 / ( v + 500 ) = .7

.8 v + 150 = .7 v + 350

.1 v = 200

v = 2000 mL

b )

Let the volume of solution A  required be v . The volume of solution of B required will be 100 - v

v x .8 + ( 100 - v ) x .3 / 100 = .5

.8 v + 30 - .3 v = 50

.5 v = 20

v = 40 mL

volume of solution B = 60 mL .

c )

It is not possible because 90 % is more than 80 % the concentration of solution A . Any mixture will have concentration less than 80 % .

volume of solution B = 60 mL

stops on an even number.