Question

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

Answer 1

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:
`x+y=q`

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.