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.