Wendy, the chemist, had a test tube containing a mixture of acid and water. She added an ounce of water, resulting in a mixture that was 20% acid. Then, she added an ounce of acid to that new mixture, and the result was 33⅓% acid. What was the percentage of acid in the original mixture?
At the start: a is the ounces of acid, while w is the ounces of H_{2}O and
acid  =  x  . 
total mixture  100 
So (I) 


Then (II), 


Then (III), 

Shaking these out, we have
(I) 100a = x(a + w),
(II) 100a = 20(a + w + 1), and
(III) 3(a + 1) = a + w + 2 → 3a + 3 = a + w + 2 → 2a + 1 = w.
(II) 100a = 20(a + w + 1), and
(III) 3(a + 1) = a + w + 2 → 3a + 3 = a + w + 2 → 2a + 1 = w.
Plug (III) into (II):
100a = 20(a + 2a + 1 + 1)
→ 100a = 20(3a + 2)
→ 100a = 60a + 40
→ 40a = 40
→ a = 1 and w = 2a + 1 = 3.
→ 100a = 20(3a + 2)
→ 100a = 60a + 40
→ 40a = 40
→ a = 1 and w = 2a + 1 = 3.
So, returning to the initial (I) above,
a  =  x  →  1  =  1  =  x  , so she started with a 25% solution. 
a + w  100  1 + 3  4  100 