SOLUTION: A coffee shop decides to blend a coffee that sells for $12 per pound with a coffee that sells for $9 per pound to produce a blend that will sell for $10 per pound. How much of each

Question 193316: A coffee shop decides to blend a coffee that sells for $12 per pound with a coffee that sells for $9 per pound to produce a blend that will sell for $10 per pound. How much of each should be used to yield 20 pounds of the new blend?
Found 2 solutions by Mathtut, nerdybill:
Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
let x and y be the amount of 12 and 9 dollar coffee respectively
:
x+y=20...........eq 1
12x+9y=10(20)....eq 2
:
rewrite eq 1 to x=12-y and plug it into eq 2
:
12(20-y)+9y=200
:
240-12y+9y=200
:
-3y=-40
:
y=13.33 pounds of 9 dollar coffee
:
x=20-13.33=6.67 pounds of 12 dollar coffee
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
A coffee shop decides to blend a coffee that sells for $12 per pound with a coffee that sells for $9 per pound to produce a blend that will sell for $10 per pound. How much of each should be used to yield 20 pounds of the new blend?
.
Let x = pounds of $12 per pound coffee
then
20-x = pounds of $9 per pound coffee
.
12x + 9(20-x) = 10(20)
12x + 180 - 9x = 200
3x + 180 = 200
3x = 20
x = 20/3
x = 6 and 2/3 pounds of $12 per pound coffee
.
Amount of $9 per pound coffee:
20-x = 20-20/3 = 60/3 - 20/3 = 40/3
or
13 and 1/3 pounds of $9 per pound coffee
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