How to adjust 60 percent wine to 40 percent?Assuming that the original amount of 60 percent alcohol was <V> 1>, to make a 40 percent alcohol, the amount of diluted liquid (such as water) added was <V> 2>.
According to the definition of alcohol content, the amount of pure alcohol = the total amount of solution × alcohol content.
In the original 60% alcohol, the amount of pure alcohol was 0.6V.
After mixing, the total amount of the solution becomes <<V1 + V2>>, and the alcohol content after mixing is 40 degrees, so the pure alcohol content after mixing is <<0.4>(V1 + V2)>.
Because the amount of pure alcohol did not change before and after mixing, the equation was:
\(0.6V_1=0.4(V_1+V_2)\)
\(0.6V_1 = 0.4V_1+0.4V_2\)
\(0.6V_1 - 0.4V_1=0.4V_2\)
\(0.2V_1 = 0.4V_2\)
\(V_2=\frac{0.2V_1}{0.4}=\frac{1}{2}V_1\)。
Therefore, to adjust the 60 percent alcohol to 40 percent alcohol, the amount of diluted liquid (such as water) needed to be half of the original 60 percent alcohol.
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How much water does a catty of 62 percent wine add to 42 percent wine?1. First, the relationship between the calculation of alcohol content and the amount of alcohol was clarified.
- The alcohol content refers to the volume percentage of alcohol in the wine (at 20 ° C). For example, 62 percent alcohol meant that 100 milliliters of alcohol contained 62 milliliters of alcohol, and 42 percent alcohol meant that 100 milliliters of alcohol contained 42 milliliters of alcohol.
- According to the formula: Alcohol amount (g)= alcohol consumption (ml) x alcohol content (%) x 0.8. For a wine with a alcohol content of 62%, let's set its volume as [V1](1 jin of wine is converted to volume here because the alcohol content is based on volume ratio, 1 jin = 500 ml), and its alcohol content is [m1 = V1 'time62'%' time0.8].
- Assuming that the volume of water added is <V2>, the total volume is <V1 + V2>, and the alcohol content of the 42% alcohol is calculated according to the formula <m1>=(V1 + V2)<times42> %<times0.8>.
2. Then, he calculated the amount of water to be added:
- It is known that the alcohol content of 62% alcohol is 500 grams per milliliter.
- Assuming that the total volume of 42% alcohol is <V>, since the amount of alcohol is the same, so <248>=<V>= V <= V>= V>=
- Then the volume of water needed to be added was [V2 = V-V1 = 732.14 - 500 = 232.14] ml.
Therefore, a catty of 62% alcohol mixed with about 232.14 ml of water could get a 42% alcohol.
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