Answer:
Part a) 2,000 mL of solution A
Part b) 40 mL of solution A and 60 mL of solution B
Part c) Is not possible
Step-by-step explanation:
Part a) How many mL of Solution A must be added to 500 mL of Solution B in order to produce a 70% acid solution?
Remember that
[tex]80\%=80/100=0.80[/tex]
[tex]30\%=30/100=0.30[/tex]
[tex]70\%=70/100=0.70[/tex]
Let
x ---->mL of solution A n 80% acid solution
y ---->mL of solution B n 30% acid solution
we know that
[tex]0.80x+0.30y=0.70(x+y)[/tex]
Remember that
[tex]y=500\ mL[/tex] ----> equation B
substitute equation B in equation A
[tex]0.80x+0.30(500)=0.70(x+500)[/tex]
solve for x
[tex]0.80x+150=0.70x+350\\0.10x=200\\x=2,000\ mL[/tex]
Part b) How many mL of Solution A and how many mL of Solution B must be combined to form a 100 mL solution that is 50% acid?
Remember that
[tex]80\%=80/100=0.80[/tex]
[tex]30\%=30/100=0.30[/tex]
[tex]50\%=50/100=0.50[/tex]
Let
x ---->mL of solution A n 80% acid solution
y ---->mL of solution B n 30% acid solution
we know that
[tex]0.80x+0.30y=0.50(100)[/tex] ----> equation A
[tex]x+y=100[/tex] -----> equation B
Solve the system by graphing
Remember that the solution is the intersection point both graphs
using a graphing tool
The solution is (40,60)
see the attached figure
therefore
40 mL of solution A and 60 mL of solution B
Part c) Is there a combination of Solution A and Solution B that is 90% acid?
Is not possible , because 90% is greater than 80% of solution A and greater than 30% of solution B
The percentage of the final concentration must be less than 80% and more than 30%
