Answer:

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.