Amerchant wants to blend 80 pounds of cacao worth $9.00 a pound from two kinds: one at $11.40 a pound and the other at $7.80 a pound. how many pounds of each kind should he mix?

The merchant should mix 53.33 pounds of cheaper cacao and 26.67 pounds of costlier cacao.

Step-by-step explanation:

A merchant wants to blend 80 pounds of cacao worth $9.00 a pound from two kinds: one at $11.40 a pound and the other at $7.80 a pound.

Let the number of pounds of cheaper cacao be x

Let the number of pounds of costlier cacao be y

The merchant wants total pounds = 80

So, first equation becomes:

or

Now values of per pounds become and

As the merchant wants the mixture worth $9 so second equation becomes:

=>

Substituting in second equation, we get

=>

=>

pounds

We know,

=> pounds

So, The merchant should mix 53.33 pounds of cheaper cacao and 26.67 pounds of costlier cacao.

We can check this:

dollars