help word problem

Question

Theresa Morgan, a chemist, has a 10% hydrochloric acid solution and a 55% hydrochloric acid solution. How many liters of each should she mix to get 1890 liters of a hydrochloric acid solution with a 50% acid concentration?

____liters of 10% hydrochloric acid solution .

 ____liters of 55% hydrochloric acid solution .

Answer 1

1890/9=210 liters 10%

1890-210= 1680 liters 55%

55-50=5

50-10=40

40/5=8=1680/210

8 times as much 55 as 10 is needed

1680=8 times 210

8/9= 8 times 1/9

210= 1/9 of 1890

.1(210)+.55(1680)

=21+924=945 liters of pure acid

=.50(1890)=945 liters of pure acid

more conventional solution method is set up this equation

.55(1890-x)+.10x =.5(1890)

simplify and solve for x=amount of 10%

1039.5-.55x +.1x=945

.45x = 1039.5-945

x=94.5/.45=210 liters of 10%

1890-x= 1680 liters 55%

yield 1890 liters 50%