Question

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. How many pounds of each kind should he mix?

Answer 1

Answer:

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:

$x+y=80$ or $x=80-y$

Now values of per pounds become $7.80x$ and $11.40y$

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

$7.80x+11.40y=9(80)$

=> $7.80x+11.40y=720$

Substituting $x=80-y$ in second equation, we get

$7.80(80-y)+11.40y=720$

=> $624-7.80y+11.40y=720$

=> $3.60y=96$

$y=26.67$ pounds

We know, $x=80-y$

=> $x=53.33$ pounds

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

We can check this:

$53.33(7.80)+26.67(11.40)=720.012$ dollars

Answer 2

answer-

he should mix 16lbs of the 7.80 mix and 8lbs of the 11.40 mix

Step-by-step explanation:

hope this helps:) btw im a student at rsm and i got this for homework so ya. your welcome also, ik the answers wrong ...s i g h...