High School

Hector was making a solution. He put the components of the solution into a beaker. Hector wanted to increase the amount of his solution while keeping the composition of the solution the same. The new solution will have 84 kilograms of water.

What will be the mass of the sugar in the new solution, in kilograms?

**Hector's Solution:**

| Component | Mass |
|-----------|-----------|
| Sugar | 9.6 kg |
| Salt | 7.0 kg |
| Water | 12.0 kg |

**Options:**

A. 24.6 kg
B. 39.6 kg
C. 49.0 kg
D. 67.2 kg
E. 98.0 kg

Answer :

Final answer:

The mass of sugar that should be mixed with the 84 kg of water in Hector's new solution, while maintaining the same composition, is 67.2 kg.

Explanation:

From the initial data given, we see that the mass of sugar is 9.6 kg and the mass of water is 12.0 kg in Hector's original solution. As Hector wants to keep the composition of the solution the same while increasing it, we use these mass ratio of sugar to water, 9.6/12.0 = 0.8, as a constant for the new solution. In the new solution, Hector will have 84 kg of water. We now need to find the mass of sugar that should be mixed with this 84 kg of water while maintaining the same composition. To do this, we can multiply the mass of water in the new solution by the determined ratio (0.8). This equals 84 kg * 0.8 = 67.2 kg. So, the mass of sugar in the new solution will be 67.2 kg.

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