Question 915878: A grocer wants to mix two kinds of coffee. One kind sells for $2.15 per pound and the other sells for 2.45 per pound. He wants to mix a total of 18 pounds and sell it for $2.30 per pound. How many pounds of each kind should he use in the new mix?
Answer by AlgebraLady88(44)   (Show Source):
You can put this solution on YOUR website! This grocer is mixing two kinds of coffee. I always love the smell of coffee!
We will say that x sells for $2.15 per pound and y sells for $2.45 per pound.
Altogether there are 18 pounds of coffee he is selling.
The algebraic equation would be x + y = 18
At $2.30 per pound, he will make 18 * $2.30 = $ 41.40
So, how many of the x and y kinds of coffee should he use to make the $2.30 per pound mixture which will net him $41.40?
The algebraic equation would be 2.15x + 2.45y = 41.40
We now have two equations :
x+y = 18
2.15x + 2.45y = 41.40
Substituting x= 18 -y in the second equation gives us
2.15(18-y) + 2.45y = 41.40
38.70 - 2.15y + 2.45y = 41.40
38.70 + 0.3y = 41.40
0.3y = 41.40 - 38.70
0.3y= 2.70
y=9
If y=9, then x= 9 as well.
So, he will use 9 pounds of the $2.15 per/lb one and another 9 pounds of the $2.45per/lb one.
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