What amout of percentage should be added to the ratio?

[scarmcadds]

Sam wants to convert a mixture of acid and water in the ratio 16 : 19 to 19 : 16. What is the amount of acid as a percentage of initial solution that should be added to achieve the required ratio?

 

[skeeter]

starting with 16 units of acid + 19 units of water = 35 total units

initial mixture is $\dfrac{16}{35} \approx 45.7$% acid and $\dfrac{19}{35} \approx 54.3$% water

add x units of acid ...

(16+x) units of acid + 19 units water = (35+x) units of new mixture

need to add x amount of acid such that $\dfrac{16+x}{35+x} = \dfrac{19}{35}$ and $\dfrac{19}{35+x} = \dfrac{16}{35}$

solving either equation for x will give the requisite number of original units of acid to be added ... just recall the question asks for the added x as percentage of the original number of units in the starting mixture.