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

In summary, the conversation discusses the pricing of paint mixtures containing different levels of pigment. A mixture with 25.0% pigment and water sells for $18.00/kg, while a mixture with 12.0% pigment sells for $10.00/kg. The question is raised about how much a blend with 17.0% pigment should be sold for to yield a 10% profit. The conversation also mentions the potential missing information about production costs and profit margins for the other mixtures. The final response suggests using an interactive math program to solve for the selling price of the 17.0% pigment blend.
  • #1
jimithing
26
0
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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  • #2
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.
 
  • #3
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
 
  • #4
"Interactive math program"?
 

What is material balance question?

Material balance question is a common problem-solving technique used in science and engineering to determine the quantity of a substance present in a system. It involves analyzing the inputs and outputs of a system to calculate the balance of the substance.

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