# A 50.0-kg mixture of salt and water is 15.0% (by mass) salt. What is the mass of salt and water in the mixture?

##### 1 Answer

Your solution contains

#### Explanation:

You know that your mixture is **by mass**, so make sure that you understand what that means before moving forward.

For a component of a mixture, its **percent concentration by mass** is calculated by dividing the **mass** of that component by the **total mass of the mixture**, and multiplying the result by

#color(blue)("% component" = "mass of that component"/"total mass of the mixture" xx 100)#

In your case, the mixture is a solution of salt and water. You know that the **total mass** of the mixture is equal to

That means that **for every** **proportion** between the mass of salt and the total mass of the mixture will help you find the mass of salt in **any amount of solution**.

In your case, you have

#50.0 color(red)(cancel(color(black)("kg solution"))) * overbrace("15.0 kg salt"/(100color(red)(cancel(color(black)("kg solution")))))^color(purple)("15.0% by mass") = color(green)("7.50 kg salt")#

Since the total mass of the solution can be written as

#m_"solution" = m_'water" + m_"salt"#

you can say that you solution will also contain

#m_"water" = "50.0 kg" - "7.50 kg" = color(green)("42.5 kg water")#