In the previous post, we have discussed three examples on how to solve mixture problems. In this post, we are going to learn how to set up the givens in a mixture problem in a table, so it is easier to solve.  Let’s have the fourth example.

Example 4

How many liters of pure water must be added to 15 liters of a 20% salt solution to make a 5% salt solution?

Solution and Explanation

In the first column, we placed the liquid or solution. We have three kinds: water, the liquid with 20% salt, and liquid with 5% salt. In the second column, we place the volumes of ths liquid. We do not know the volume of water, so we represent it with x. Since we have to combine water with 20% salt solution, we have to add the volumes of the two liquid.  This makes sense since if we add more water, the amount of salt is getting lesser in relation to the total volume of the liquid.

Again, the total amount of salt when water is combined with 20% salt solution should also be equal to the total amount of salt in the 5% salt solution. That means that in the last column, we have to add the first and the second row and then equated to the third row.  That is,

3 = 0.05(x + 15)

3 = 0.05x + 0.75

2.25 = 0.05x

45 = x

That means that we need 45L of water to turn a 20% salt solution to a 5% solution.

Check:

3 = 0.05(x + 15)

3 = 0.05(45 + 15)

3 = 0.05(60)

3 = 3