college algebra

Question

A coffee distributor needs to mix a(n) Ethiopian coffee blend that normally sells for $8.10 per pound with a Breakfast coffee blend that normally sells for $14.30 per pound to create 80 pounds of a coffee that can sell for $12.67 per pound. How many pounds of each kind of coffee should they mix?

 Write an equation using the information as it is given above that can be solved to answer the question. Use as your variable to represent the quantity of Ethiopian coffee blend.

 ? pounds of the Ethiopian Blend 

 ? pounds of the Breakfast Blend. 

Round your answers to the nearest whole number of pounds.

Answer 1

Hello, thank you for taking the time to post your question!

The key on this type of question is that you want to use the information given in order to set up an algebraic expression that relates the variables with one another. In this scenario we have

8.10x + 14.30(80 – x) = 12.67(80)  because he’s mixing together the $8.10 coffee with the $14.30 coffee to get one that costs $12.67. and in total he has 80 pounds to work with between the two

Solving that equation for x yields

8.10x + 1144 – 14.30x = 1013.6

-6.2x = -130.4

x = -130.4/-6.2 = 21.03

rounded to the nearest whole number that would mean 21 pounds in the Ethiopian Blend, then (80 – 21) = 59 pounds in the Breakfast Blend in order to hit his desired price point

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

x + y = 80

8.1x + 14.3y = 12.67*80 = 1013.6

8.1 x + 14.3 * (80-x) = 1013.6

8.1 x + 1144 - 14.3 x = 1013.6

-6.2x = -130.4

x = 21.032258064516129032258064516129‬

y =58.967741935483870967741935483871‬

y = 59

8.1*21 + 14.3*59 =