How do you create your equations when working on a mixture word problem?

1 Answer
May 27, 2015

Let's try to think about the general form of a word problem involving mixtures.

In general, we have the following scenario:

  • a merchant sells two kinds of products (coffee, sweets, etc).
  • we know the unit prices for both kinds of products and for the final mixture
    #p_1# US dollars per pound for the first kind of product,
    #p_2# US dollars per pound for the second kind of product
    #p_m# US dollars per pound for the mixture

  • we know the total quantity formed by the mixture of the two products (#q# pounds)

  • we have to find out the quantities of each product needed to form the mixture
    (here we have the variables: #x# denoting the quantity of the first kind of product and #y# denoting the quantity of the second kind of product)

Now, we have sufficient information to work out the equations.

First, we know that the sum of the two quantities is #q# pounds, which gives us the first equation:

Second, we know that the sale price is the product of quantity and unit price, which gives us the second equation:
#p_1 x + p_2 y = p_m*q#

Now, we have a system of two linear equations that can be easily solved by substitution.