# Question #2b6d2

##### 1 Answer

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

Solve this equation for

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

#100 * m_"water" = 76 + 95 * m_"water"#

#5 * m_"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")#