A merchant has coffee worth 3dollars a pound that she wishes to mix with 3 pounds of coffee worth 9dollars a pound to get a mixture that can be sold for 6dollars a pound. How many pounds of the 5 dollar coffee should be used?
3x + 9(3) = 6(x+ 3)
3x + 27 = 6x + 18
-3x =-9
x = 3
To solve this problem, we can use a weighted average formula.
Let's assume that the merchant needs to mix x pounds of $5 coffee with the existing 3 pounds of $9 coffee.
Given that the merchant wants to sell the mixture for $6 per pound, we can set up the equation:
(3 * 9 + 5 * x) / (3 + x) = 6
To solve for x, we can cross-multiply:
(3 * 9 + 5 * x) = 6 * (3 + x)
Simplifying the equation:
27 + 5x = 18 + 6x
Combining like terms:
5x - 6x = 18 - 27
-x = -9
Dividing by -1 to isolate x:
x = 9
So, the merchant should use 9 pounds of the $5 coffee to obtain the desired mixture.