A solution contains 60% sugar. If 15 liters of the solution is diluted with wate

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Question: A solution contains 60% sugar. If 15 liters of the solution is diluted with water to make it 40% sugar, how much water is added?

Options:

Correct Answer: 15 liters

Solution:

Let x be the amount of water added. 0.6 * 15 = 0.4 * (15 + x). Solving gives x = 15 liters.

A solution contains 60% sugar. If 15 liters of the solution is diluted with water to make it 40% sugar, how much water is added?

A solution contains 60% sugar. If 15 liters of the solution is diluted with water to make it 40% sugar, how much water is added?

Step 1: Understand that we have a solution that is 60% sugar and we have 15 liters of it.
Step 2: Calculate the amount of sugar in the 15 liters of solution. This is done by multiplying 15 liters by 60% (or 0.6). So, 15 * 0.6 = 9 liters of sugar.
Step 3: Let 'x' be the amount of water we will add to the solution.
Step 4: After adding 'x' liters of water, the total volume of the new solution will be 15 + x liters.
Step 5: We want the new solution to be 40% sugar. This means that the amount of sugar (which is still 9 liters) should equal 40% of the new total volume (15 + x). So we set up the equation: 9 = 0.4 * (15 + x).
Step 6: Solve the equation from Step 5. First, multiply both sides by 10 to eliminate the decimal: 90 = 4 * (15 + x).
Step 7: Distribute the 4 on the right side: 90 = 60 + 4x.
Step 8: Subtract 60 from both sides to isolate the term with 'x': 30 = 4x.
Step 9: Divide both sides by 4 to solve for 'x': x = 30 / 4 = 7.5 liters.
Step 10: Therefore, the amount of water added is 7.5 liters.

Concentration and Dilution – Understanding how to calculate the concentration of a solution before and after dilution.
Algebraic Manipulation – Using algebra to set up and solve equations based on the relationships between quantities.