How do you create your equations when working on a mixture word problem?
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 (
- 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
Second, we know that the sale price is the product of quantity and unit price, which gives us the second equation:
Now, we have a system of two linear equations that can be easily solved by substitution.