How many liters of a 20% alcohol solution must be mixed with 20 liters of a 70% solution to get a 40% solution

30 liters of solution must be mixed.

Step-by-step explanation:

Given:

Amount of solution (70%) = 20 Liters

Amount of 20% alcohol solution = A

Find:

Amount of 20% alcohol solution to get 40% solution

Computation:

Amount of 20% alcohol solution to get 40% solution :

⇒ 20% (A) + 70% (20) = 40% (A + 20)

⇒ 0.2 A + 14 = 0.4 A + 8

⇒ 14 - 8 = 0.4 A - 0.2 A

⇒ 6 = 0.2 A

⇒ A = 30 Liter

30 liters of solution must be mixed.

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb