Question

From a mixture of vinegar and water which is 20% vinegar, 2 quarts are removed and replaced by pure vinegar. The resulting mixture is 49% vinegar. Find the number of quarts in the original mixture.

a) 4 quarts
b) 5 quarts
c) 6 quarts
d) 8 quarts

Answer 1

By setting up an equation based on the percentage of vinegar before and after the removal and addition of vinegar, we can solve for x, which represents the number of quarts in the original mixture. The calculations lead to an approximate value of 5.517, suggesting that the original mixture contained roughly 5 quarts of the vinegar and water mixture.

Step-by-step explanation:

To solve for the number of quarts in the original mixture, let's assume there were x quarts in the original mixture. Initially, the mixture is 20% vinegar, so the amount of vinegar in the mixture is 0.20x quarts. When 2 quarts are removed, the amount of vinegar removed is 0.20 * 2 = 0.40 quarts. Therefore, the amount of vinegar left in the mixture is 0.20x - 0.40 quarts. Then, 2 quarts of pure vinegar are added to the mixture. This means the new amount of vinegar in the mixture is (0.20x - 0.40) + 2. The resulting mixture is 49% vinegar of x quarts, so the equation is 0.49x = (0.20x - 0.40) + 2.

Solving this equation:

1. 0.49x = 0.20x + 1.60
2. 0.49x - 0.20x = 1.60
3. 0.29x = 1.60
4. x = 1.60 / 0.29
5. x = 5.517 (approximately)

Therefore, the original mixture was closest to 5 quarts, which is option (b).