# What amout of percentage should be added to the ratio?

• MHB
In summary, to achieve a ratio of 19 : 16 for a mixture of acid and water initially in the ratio 16 : 19, x units of acid should be added, where x is equal to the initial amount of acid as a percentage of the total initial solution. This can be calculated by solving either of the equations $\dfrac{16+x}{35+x} = \dfrac{19}{35}$ or $\dfrac{19}{35+x} = \dfrac{16}{35}$ and recalling that the question asks for x as a percentage of the initial amount of acid.
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?

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.

## 1. What is a ratio?

A ratio is a comparison of two numbers or quantities. It shows the relationship between the two values and is typically expressed in the form of a fraction or with a colon (:).

## 2. Why would you need to add a percentage to a ratio?

Adding a percentage to a ratio can help adjust the ratio to better reflect a particular situation or to make it more accurate. For example, if the original ratio is based on a small sample size, adding a percentage can help make it more representative of the larger population.

## 3. How do you calculate the percentage to be added to a ratio?

The percentage to be added to a ratio can be calculated by multiplying the original ratio by the percentage in decimal form. For example, if the original ratio is 2:5 and you want to add 20%, you would multiply 2:5 by 0.2 to get a new ratio of 2.4:5.

## 4. Is there a specific amount or percentage that should be added to a ratio?

There is no specific amount or percentage that should be added to a ratio. The amount to be added will depend on the specific situation and what is needed to make the ratio more accurate or representative.

## 5. Can a percentage be subtracted from a ratio instead of added?

Yes, a percentage can be subtracted from a ratio just as it can be added. The process is the same, but instead of multiplying by a decimal greater than 1, you would multiply by a decimal less than 1 to get a smaller ratio.

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