# How do you solve mixture problems using system of equations?

##### 1 Answer

Just to make it easier for me, I usually make a small table with the headings **"Components", "Unit Value", "Amount" and "Value".**

Consider the following question:

**How many pints of 20% acid solution and 70% acid solution must be mixed to obtain 40 pints of 50% acid solution? **

First, I'll set up my table. I'll fill in the unknowns with variables

From this, we can easily set up the two equations.

Sum of values of two acids = Value of mixture

Therefore,

For convenience, we'll multiply the entire equation by 10,

This is equation **(1)**

Setting up the second equation,

Sum of amounts of each acid = Amount of mixture

To make at least one term of this equation identical to a term of equation (1), we'll multiply the entire equation by 2,

This is equation **(2)**

Subtracting equation **(2)** from **(1)**,

Thus,

Substituting **(2)**,

So, we have

We can conclude that 16 pints of 20% acid solution must be mixed with 24 pints of 70% solution to obtain 40 pints of 50% solution.

*I hope your question was answered.*