Help with math problem solving question?

Question

Bill, a health-food enthusiast, is mixing concoctions in his basement. He's invented a new drink that needs to be 40% carrot juice and 60% other stuff. He has been to the store and has found some concentrated carrot juice (60% carrot juice). His neigbor Clara, who decided one day that she dosnt like carrot juice anymore has contributed 80 quarts of 12% carrot juice. How many quarts of the concentrated carrot juice does he need to add to the 80 quarts of weak juice to produce his perfect drink with 40% carrot juice?

please show a lil work.. THANKSSSSS

Answer 1

Let say he needs X quarts of 60% juice.
So we have 0.4X quarters stuff + 0.6X quarters carrot.
From the weak we have 0.88x80 quarters stuff + 0.12x80 quarters carrot.
Like to say, (0.6X+9.6) quarters carrot in (80+X) quarters juice 40%

(0.6X+9.6)/(80+X) = 0.4

solving this equation the answer is X=112 quarters

Answer 2

let Bill need x quarts of 6o% carrot juice to be mixed with 80 quarts of12% carrot juice to get 80+x quarts of 40% juice.
so,
0.60*x+012*80=0.40(x+80)
=>0.6x+.9 .6=0.40x+32
=>0.60x-0.40x=32-9.6
=>0.20x=22.4
=>x=22.4/0.20=112
Bill needs to mix 112 quarts of concentrated carrot juice to be mixed

Answer 3

try (80*.12)+(x*.6) = (80+x)*0.40

Just rearrange and solve for x