SOLUTION: The store manager decides to make 40lbs of blend of coffees that he plans to sell for 10 dollars a lb. He mixes some coffee that sells for 9 dollars a lb with coffee that sells for

Question 993666: The store manager decides to make 40lbs of blend of coffees that he plans to sell for 10 dollars a lb. He mixes some coffee that sells for 9 dollars a lb with coffee that sells for 12 dollars a lb. How much of each should he use? (Hint- one coffee is x and the other coffee of the rest of the mixture so use 40 - x for the amount)
I already calculated that 40 lbs of coffee costing 10 dollars a lb would be 400 dollars. Now I need help on how to calculate how many pounds adding up to 40lbs. I would use of each that would bring me to 400 dollars total.
Thank you!
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x is the amount of coffee at 9 dollars a pound.
y is the amount of coffee at 12 dollars a pound.

you have two equations:

x + y = 40

9x + 12y = 400

solve these equations simultaneously, and you will get:

x = 26.67
y = 12.33

x + y = 40 becomes 26.67 + 13.33 = 40

9x + 12y = 400 becomes 9 * 26.67 + 12 * 13.33 which becomes 240.03 + 159.96 which becomes 299.99.

the difference from 400 is due to rounding.

26.67 is really 26.6666666666666........

13.33 is really 13.333333333333333........

to get this solution, you need to be able to solve the system of equations simultaneously.

here's a reference on how to do that.

http://www.regentsprep.org/regents/math/algebra/ae3/indexAE3.htm

i'll use elimination method.

your two equations are:

x + y = 40
9x + 12y = 400

multiply both sides of the first equation by 9 to get:

9x + 9y = 360
9x + 12y = 400

subtract the first equation from the second equation to get:

3y = 40

divide both sides of this equation by 3 to get:

y = 13.33.....
this rounds to 13.33
use that value of y to solve for x in either equation to get:

x = 26.66.....
this rounds to 26.67

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
The store manager decides to make 40lbs of blend of coffees that he plans to sell for 10 dollars a lb. He mixes some coffee that sells for 9 dollars a lb with coffee that sells for 12 dollars a lb. How much of each should he use? (Hint- one coffee is x and the other coffee of the rest of the mixture so use 40 - x for the amount)
I already calculated that 40 lbs of coffee costing 10 dollars a lb would be 400 dollars. Now I need help on how to calculate how many pounds adding up to 40lbs. I would use of each that would bring me to 400 dollars total.
Thank you!

Since you wish to use x for the amount of one of the blends, then we'll make the amount of the $9/lb-blend to mix, be x
Then amount of the $12/lb-blend to mix is: 40 - x
We then get the following equation:
9x + 12(40 - x) = 40(10)
9x + 480 - 12x = 400
- 3x = 400 - 480
- 3x = - 80
x, or amount of $9/lb-blend to mix = , or lbs
Amount of $12/lb-blend to mix: , or lbs
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