How many gallons of acid must be added to G gallons of a k% acid solution to bring it up to an m% solution?

Question

A: G/(100-m)

B: Gm/(100-m)

C: G(m-k)/(100-m)

D: 100-m/G(m-k)

Answer 1

Two solutions presented:

Solution 1:

Note that when m = k, then the answer should be zero. Of the four that we are to choose from, only C gives zero.

Solution 2:

Let g = number of gallons of (100%) acid to add.

G gallons of k% acid solution has kG/100 gallons of (100%) acid, with the remainder being water.

Our goal to to combine these liquids in such a way that we end up with G+g gallons of m% acid.

The equation we must solve is then:

Total gallons of acid = g + (k/100)*G = (m/100)*(g+G)

Solve for g:

g - (m/100)g = (m/100)G - (k/100)G

g*(1 - m/100) = (G/100)*(m - k)

g = (G/100)*(m - k) / (1 - m/100) = G(m - k) / (100 - m)