A solution problem?

Question

Let 0
You are not suppose to solve the values, because you cant.

so uh... whats the answer? you kinda lost me there at the end

Answer 1

no of liters required= (ab%-m. c%)/a%
i.e. (ab/100-m.c/100) / (a/100)

Answer 2

Ok lets assume you add x liters of solution a and y liters of solution c. Then the total volume of the final solution is z. So x+y=z. Because z is not given lets assume it is 1. Then x+y=1 or 1-y=x

Now if the final solution b% of a substance then it means that there are b liters of the substance per liter of the substance. The same is true for both mixtures a and c. This gives us the equation
Vol(of a)*a%+Vol(c)*c%=Vol(b)*b%
using x,y,z and multiplying by 100 gives us:
xa+yc=zb but we said z= 1 and x = 1-y
(1-y)a+yc=b
a+(c-a)y=b
y=(b-a)/(c-a)

Answer 3

(b/100)(m + x) = (a/100)x + (c/100)m
(b(m + x))/100 = (ax + cm)/100

b(m + x) = ax + cm
bm + bx = ax + cm
bx - ax = cm - bm
x(b - a) = m(c - b)
x = (m(c - b))/(b - a)
x = (m(-b + c))/(-a + b)
x = (m(-(b - c)))/(-(a - b))
x = (-m(b - c))/(-(a - b))
x = (m(b - c))/(a - b)

So if you were given the solutions of a, b, and c, then you could find out what x is

x = number of liters