What amout of percentage should be added to the ratio?

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To convert a mixture of acid and water from a ratio of 16:19 to 19:16, Sam must determine the amount of acid to add as a percentage of the initial solution. The initial mixture consists of 16 units of acid and 19 units of water, totaling 35 units. The initial acid concentration is approximately 45.7%, and the required calculations involve solving the equation $\dfrac{16+x}{35+x} = \dfrac{19}{35}$ to find the value of x, which represents the units of acid to be added.

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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?
 
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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.
 

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