Let [tex]x,y[/tex] denote the volume of the 75% and 90% solutions to use, respectively. We want to end up with a 360L solution, so [tex]x+y=360[/tex].
We want this new solution to have an 85% concentration so that it would contain 0.85*360L = 306L of antifreeze. The volume of antifreeze contributed by the reagent solutions are [tex]0.75x[/tex] and [tex]0.9y[/tex], and their total should match the new solution's total volume of antifreeze, so that [tex]0.75x+0.9y=306[/tex].
Solve this system and you get [tex]x=240\,\rm L[/tex] and [tex]y=120\,\rm L[/tex].
Answer:
240 liters
Step-by-step explanation:
Let x be the quantity of 75% antifreeze solution and y be the quantity of 90% antifreeze solution,
Since, the total quantity of the mixture = 360,
⇒ x + y = 360 ----- (1),
Also, the resultant solution is of 85% antifreeze solution,
⇒ 75 % of x + 90% of y = 85% of 360
0.75x + 0.90y = 0.85 × 360
0.75x + 0.90y = 306
75x + 90y = 30600 -----(2),
Equation (2) - 75 × equation (1),
We get,
15y = 3600
⇒ y = 240
Hence, 240 liters of 90% solutions will be used.
