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A merchant has coffee worth $30 a pound that she wishes to mix with 80 pounds of coffee worth $90 a pound to get a mixture that she will sell for $70 a pound. How many pounds (lb) of the $30 coffee should be used?

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fmorelos

Answer:

You need 40 pounds of the $30 coffee.

Explanation:

You need to calculate a weighted average for the $30/pound coffee and $90/pound coffee and equalize it to $70:

[tex]\frac{x*30 + 80 pounds * 90}{x+80} = 70[/tex]

[tex]30x + 7200 = 70(x +80) = 70x + 5600[/tex]

[tex]40x = 1600[/tex]

[tex]x = 40[/tex]

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