Gabe Amodeo, a nuclear physicist, needs 60 liters of a 40% acid solution. He currently has a 20 % solution and a 50 % solution. How many liters of each does he need to make the needed 60 liters of 40% acid solution?

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

answer: 12/52

step-by-step explanation: my reasoning is that there are 12 face cards in a deck and a total of 52 cards in all.