Problema Solution
An 80% of acid solution is to be mixed with a 30% solution to get 90 gallons of a 50% solution. How many gallons of each solution are needed?
Answer provided by our tutors
Let's call olution A and B,
Now, A + B = 90 gallons, (i)
because, the total amount of solution is summation of both.
but, 80 % of A and 30% of B is needed to make 50 % solution.
0.8 A + 0.3 B = 0.5 ( A + B)
0.8 A + 0.3 B = 0.5 x 90 ( see (i) )
0.8 A + 0.3 B = 45
8 A + 3 B = 450(ii)
now, multiplying ( i ) with 3,
3A + 3B = 270,(iii)
subtracting (iii) from (ii),
5A = 280,
So, A = 56 and, B= 90 - A = 90 - 56 = 34 ( from (i) )