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

x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

step-by-step explanation:

last month maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. if she hiked a total of 90 miles, which equation can be used to find the number of times maria hiked each trail? x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x