Final answer:
To solve the mixture problem, the quantity of wine replaced is calculated using the concept of weighted averages. By setting up an algebraic equation, we find that approximately 41.18 units of the original 30% alcohol wine was replaced with 13% alcohol wine to result in a mixture with 23% alcohol content.
Step-by-step explanation:
The question involves solving a mixture problem using percentages, which is a common task in Mathematics. We're given that we start with a wine jar containing 30% alcohol, and then some of the wine is replaced with another wine containing 13% alcohol. After the replacement, the mixture has 23% alcohol. To find the quantity of wine replaced, we can use the concept of weighted averages.
Let's assume the original amount of wine is 100 units (it could be any unit of measurement as long as it's consistent). After replacing x units of the original wine with x units of 13% alcohol wine, the total amount of wine remains 100 units. We can set up the equation:
0.30*(100 - x) + 0.13*x = 0.23*100
Solving for x gives us:
30 - 0.30x + 0.13x = 23
0.17x = 7
x = 7 / 0.17
x = 41.18 (approximately)
Therefore, approximately 41.18 units of the original wine were replaced with the 13% alcohol wine.