SOLUTION: A lab technician needs to make 400 kg of 51% alcohol solution by combining 60% alcohol solution by mass and 40% alcohol solution by mass. How many kilograms of the 40% solution mus

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: A lab technician needs to make 400 kg of 51% alcohol solution by combining 60% alcohol solution by mass and 40% alcohol solution by mass. How many kilograms of the 40% solution mus      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1197437: A lab technician needs to make 400 kg of 51% alcohol solution by combining 60% alcohol solution by mass and 40% alcohol solution by mass. How many kilograms of the 40% solution must be used?

Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
w, amount of 60%
400-w, amount of 40%

60w%2B40%28400-w%29=51%2A400
-
60w-40w%2B40%2A400=51%2A400
%2860-40%29w=51%2A400-40%2A400
w=%2851%2A400-40%2A400%29%2F%2860-40%29
highlight%28w=400%28%2851-40%29%2F%2860-40%29%29%29------some people know a shortcut to reach this.
Compute w.

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Follow the formal algebraic solution shown in the response from the other tutor to see how they end up with the result that the amount of 60% alcohol solution is 11/20 of the total of 400kg.

That result can be obtained much more quickly and easily without algebra by looking at the three percentages 40, 51, and 60 on a number line and observing that 51 is 11/20 of the way from 40 to 60. That immediately gives you the result that 11/20 of the mixture is the 60% alcohol solution.

ANSWER: 11/20 of 400kg, or 220kg, of the 60% solution; the other 180kg of the 40% solution.