whats the key concept here ?

Question

Here is a mixture problem ?

http://i218.photobucket.com/albums/cc298/curseofgoldendragon/mixture.png

whats the key concept here ?

see, this problem is a merging of mixture and loss/profit chapter.

hence i am getting confused

whats the key concept here ? please explain
what should be kept in mind ?
where do i start ?

Answer 1

Well, I'm not sure what the key concept is (maybe learning to translate word problems into equations?), but I can tell you where to start. With any word problem, always begin by declaring your variables. We know there are only two types of non-derived quantities in this equation: how much you pay for the beans, and how much you pay for them. So let us assign:

C₁ = the cost of one unit of fine coffee beans
C₂ = the cost of one unit of not-so-fine coffee beans
R = the revenue generated by one unit of beans (since apparently all coffee beans are sold at the same price, regardless of quality).

Now, we know that selling one unit of good coffee beans results in a loss of 4%, so we have:

R = .96 C₁

Since the mixed beans are 5 parts low quality beans to 2 parts high quality, the cost of one unit of mixed beans is (2C₁ + 5C₂)/7. Since these sell at a 20% profit, we have that:

R = 1.2 (2C₁ + 5C₂)/7.

Equating these two and solving for C₁, we have:

.96 C₁ = 1.2 (2C₁ + 5C₂)/7
6.72 C₁ = 1.2 (2C₁ + 5 C₂)
6.72 C₁ = 2.4 C₁ + 6C₂
4.32C₁ = 6C₂
432C₁ = 600 C₂
C₁ = 600/432 C₂ = 25/18 C₂

Now, substituting this result into the second equation:

R = .96 * (25/18 C₂)
R = 24/25 * 25/18 C₂
R = 24/18 C₂ = 4/3 C₂

So the profit on a unit of not-so-fine beans is 1/3 or 33 1/3%. Thus the correct answer is 2. And we are done.