What Is the Optimal Selling Price for a Paint Mixture with 17.0% Pigment?

AI Thread Summary
To determine the optimal selling price for a paint mixture with 17.0% pigment, the discussion highlights the need for additional information, particularly regarding production costs and profit margins of existing mixtures. The current mixtures with 25.0% and 12.0% pigment sell for $18.00/kg and $10.00/kg, respectively. Participants suggest making assumptions about the profit margins of these mixtures to calculate the price for the new blend. One user outlines a mathematical approach to solve for the selling price by establishing equations based on the pigment concentrations. Ultimately, the discussion emphasizes the importance of accurate cost data to arrive at a viable selling price.
jimithing
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A paint mixture containing 25.0% pigment and the balance water sells for $18.00/kg, and a mixture containing 12.0% pigment sells for $10.00/kg. If a paint retailer produces a blend containing 17.0% pigment, for how much ($/kg) should it be sold to yield a 10% profit?

Am I wrong, or are they lacking information (i.e. cost of production, etc.)
this is driving me nuts... :confused:
 
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I would say yes you are missing some information. How much profit is made on the 25% and 12% mixtures comes to mind and as you said production costs... You can make some assumptions like the 25% and 12% mixtures are sold at 10% profit or the like.

Well, good luck.
 
i assumed that the 25% and 12% mixtures were sold at cost, so i used
.25x + .75y = 18
and
.12x + .88y = 10

solved for x and y, then substituted into .17x + .83y = z
found z, multiplied by 1.1

hopefully that's what they're looking for
 
"Interactive math program"?
 
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