Question

At a municipal waste handling facility, 30 metric ton mixture of food waste, yard waste, and paper waste was available. The moisture content of this mixture was found to be 10%. The ideal moisture content for composting this mixture is 50%. The amount of water to be added to this mixture to bring its moisture content to the ideal condition is _________ \text{ metric ton.} (in integer)

Hint:

When calculating the required moisture content for composting, use a mass balance approach to relate the initial and final mass of water in the mixture.

Answer 1

Correct Answer: 24

Let the amount of water to be added be \( x \) metric tons. Initially, the mass of water in the mixture is: \[ \text{Mass of water} = 30 \times 0.10 = 3\ \text{metric tons} \] The final moisture content should be 50% of the total mass after adding \( x \) metric tons of water. Thus, the total mass of the mixture after adding water is \( 30 + x \) metric tons, and the mass of water becomes \( 3 + x \). The desired moisture content is 50%, so we set up the equation: \[ \frac{3 + x}{30 + x} = 0.50 \] Solving for \( x \): \[ 3 + x = 0.50 \times (30 + x) \] \[ 3 + x = 15 + 0.50x \] \[ 3 + 0.50x = 15 \] \[ 0.50x = 12 \quad \Rightarrow \quad x = 24 \] Thus, the amount of water to be added is: \[ \boxed{24}\ \text{metric tons} \]