Question 2b6d2

Aug 22, 2015

The final weight of the mixture is 16 kg.

Explanation:

What you're essentially doing by evaporating some water is making the mixture more concentrated, meaning that you now have the same amount of sugar in less water.

First, start by figuring out how much sugar your original mixture contained. Since this mixture was 96% water, you can be sure that you have 4% sugar

20color(red)(cancel(color(black)("kg mixture"))) * "4 kg sugar"/(100color(red)(cancel(color(black)("kg mixture")))) = "0.8 kg sugar"

This is the amount of sugar that the final mixture will contain as well, since you're only changing the amount of water present.

Let's say that the final mixture will now contain ${m}_{\text{water}}$ kilograms of water. This means that you can write

m_"water"/("0.8 kg sugar" + m_"water") * 100 = 95%

Solve this equation for ${m}_{\text{water}}$ to get the amount of water present in the final mixture

100 * m_"water" = 95 * (0.8 + m_"water")

$100 \cdot {m}_{\text{water" = 76 + 95 * m_"water}}$

$5 \cdot {m}_{\text{water" = 76 implies m_"water" = 76/5 = "15.2 kg}}$

The final mixture will contain 0.8 kg of sugar and 15.2 kg of water, which means that its final weight will be

m_"mixture" = 15.2 + 0.8 = color(green)("16 kg")#