Janet sells 'designer chocolates.' Bonbons cost $2 a pound, while truffles cost $5 a pound. Janet has five pounds of bonbons, to which she wants to add just enough truffles to result in a $3-a-pound chocolate mixture. How many pounds of truffles should she use?
Mixture problems are especially difficult, so here are some general guidelines.
There are two related 'equality concepts' that we have to apply here:
(1) the total *amounts* of each type of chocolate must equal the amount in the resulting mixture.
(2) the total *values* of the individual chocolates used must equal the value of their resulting mixture. Value is just the price multiplied by the amount used.
Let's start by letting x represent the number of pounds of truffles that we'll add to the bonbons.
If we have x pounds of truffles and 5 lbs. of bonbons? what expression, in terms of x, represents the total number of pounds in the mixture? what is the value of the mixture if its worth $3 a lb?
What is the value of x pounds of truffles? five pounds of bonbons?
Once we've answered these questions, how do we proceed?
