Question 277746: A 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?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A 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?
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Equation:
red + red = red
1.23x + 0.87(5000-x) = 1.00(5000)
Multiply thru by 100 to get:
123x + 87*5000 - 87x = 100*5000
36x = 13*5000
x = 1805.56 lbs (amt of 123% pigment needed for the mixture)
5000-1805.56 = 3194.44 lbs (amt of 87% pigment needed for the mixture)
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Cheers,
Stan H.
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