Question 182906: A local company makes pigments used to color fabrics, plastics and paints. To ensure the finished product matches the customer’s expectations, pigments of varying strength are blended to obtain what is called a “100% strength” commercial standard. The plant has 5000 pounds of Pigment Red 1 with strength of 123% of the standard, and they also have 17,890 pounds of Pigment Red 1 at 87% strength versus the same commercial standard.
Your boss wants to know how much of the 87% material is needed to blend with the 5000 pounds of the 123% material so that the final strength of the blended material is 100% strength. What do you tell him?
Sometimes he asks you how much of the low strength material is needed to mix with a known amount of high strength pigment, sometimes its how much high to blend with some low. You are tired of him asking you to answer this question for different amounts of material. How could you make it easier for yourself?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Your boss wants to know how much of the 87% material is needed to blend with the 5000 pounds of the 123% material so that the final strength of the blended material is 100% strength. What do you tell him?
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Equation:
0.87x + 1.23(5000) = 1.00(5000+x)
Multiply thru by 100 to get:
87x + 123*5000 = 5000 + x
86x = -122*5000
x = -7093.023
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There is no positive solution to the problem.
There is no amount of 123% material that can be added
to produce a 100% strenth mixture.
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Cheers,
Stan H.
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