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) )