We want 110 ml of a 35% salt solution. Our only resources are solution A that is 20% salt, and solution B that is 95% salt. Let a be the volume in ml of solution A used, and let b be the volume in ml of solution B used.
So a + b = 110 ml.
Or
b = 110 ml - a.
a × 20% + (110 - a) × 95% = 110 ml × 35%
0.2a +110×0.95 -0.95×a = 38.5 ml
104.5 ml + ( .2 -.95) a ml = 38.5 ml
Subtract 38.5 from both sides and combine (.2 - .95):
66 ml + (-.75) a ml = 0
Add -.75 a ml to both sides:
66 ml = .75 a ml
Divide by the coefficient of a:
88 ml = a
110 ml - 88 ml = 22 ml = b
22 ml × 0.95 = 20.9 ml pure salt
88 ml × 0.20 = 17.6 ml pure salt
20.9 + 17.6 = 38.5 ml pure salt
As seen above, this would be 35% salt solution in 110 ml.
And that is exactly what we set out to do.
