# Question #6f827

##### 1 Answer

#### Explanation:

The idea here is that the density of the mixture will reflect the **contribution** the volume of each substance has in the *total volume of the mixture*.

In your case, you have **equal volumes** of butter and of sand, which means that the density of the mixture will be split half way between the two densities of the components of the mixture.

Mathemcatically, you can prove this using

#rho_1 = m_1/V -># the density of butter

and

#rho_2 = m_2/V -># the density of sand

The volume

Now, the density of the mixture will be

#rho_"mixture" = m_"total"/V_"total" " "# , where

This means that you have

#rho_"mixture" = (m_1 + m_2)/(V + V) = (m_1 + m_2)/(2V)#

#rho_"mixture" = 1/2 * (m_1 + m_2)/V = 1/2 * (m_1/V + m_2/V)#

But

#rho_"mixture" = 1/2 * (rho_1 + rho_2)#

Therefore,

#rho_"mixture" = 1/2 * (0.860 + 2.28)"g/mL" = color(green)("1.57 g/mL")#