Question

A 75% antifreeze solution is to be mixed with a 90% antifreeze solution to get 360 liters of a 85% solution. How many liters of the 75% and how many liters of the 90% solutions will be used?

Answer 1

Let
`x,y` denote the volume of the 75% and 90% solutions to use, respectively. We want to end up with a 360L solution, so
`x+y=360`.

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
`0.75x` and
`0.9y`, and their total should match the new solution's total volume of antifreeze, so that
`0.75x+0.9y=306`.

Solve this system and you get
`x=240\,\rm L` and
`y=120\,\rm L`.

Answer 2

240 liters

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.