In: Math
How many liters of 20% alcohol solution should be added to 40 liters of a 50% alcohol solution to make a 30% solution?
Let x be the quantity of the 20% alcohol solution to be added to the 40 liters of a 50% alcohol. Let y be the quantity of the final 30% solution. Hence
x + 40 = y
We shall now express mathematically that the quantity of alcohol in x liters plus the quantity of alcohol in the 40 liters is equal to the quantity of alcohol in y liters. But remember the alcohol is measured in percentage term.
20% x + 50% * 40 = 30% y
Substitute y by x + 40 in the last equation to obtain.
20% x + 50% * 40 = 30% (x + 40)
Change percentages into fractions.
20 x / 100 + 50 * 40 / 100= 30 x / 100 + 30 * 40 / 100
Multiply all terms by 100 to simplify.
20 x + 50 * 40 = 30 x + 30 * 40
Solve for x.
x = 80 liters
Hence 80 liters of 20% alcohol is be added to 40 liters of a 50% alcohol solution to make a 30% solution.
Answer:80 liters of 20% alcohol is be added to 40 liters of a 50% alcohol solution to make a 30% solution.