High School

A drum is filled with a mixture of two liquids, L1 and L2, in the ratio 5:7. When 9 liters of the mixture are taken out and replaced by L1, the ratio of L1 to L2 becomes 9:7. How many liters of liquid L1 were there in the drum initially?

Answer :

Final answer:

To find the initial volume of l1 in the drum, we can set up and solve an equation using the dilution equation.

Explanation:

To solve this problem, we can set up an equation using the dilution equation: M1 L1 = M2 L2. We know that initially, the ratio of the two liquids is 5:7, so we can let the initial volume be 5x and 7x liters. After 9 liters are taken out and replaced with l1, the new ratio is 9:7. From this information, we can solve for x and find out how many liters of l1 were there initially.

Using the dilution equation, we can set up the equation: (5x - 9) / (7x) = 9/7. Cross multiplying and solving the resulting quadratic equation, we find that x = 45/16. Therefore, the initial volume of l1 is 5x = 5 * (45/16) = 281.25 liters.

Learn more about Dilution equation here:

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