What’s in a pigment?
SOLUTION: a painter wanted to mix 2 liters of blue paint with 3 liters of yellow paint to make 5 liters of green paint. however, by mistake, he used 3 liters of blue and 2 liters of yellow s
Algebra -> Polynomials-and-rational-expressions -> SOLUTION: a painter wanted to mix 2 liters of blue paint with 3 liters of yellow paint to make 5 liters of green paint. however, by mistake, he used 3 liters of blue and 2 liters of yellow s Log On
Question 1192358: a painter wanted to mix 2 liters of blue paint with 3 liters of yellow paint to make 5 liters of green paint. however, by mistake, he used 3 liters of blue and 2 liters of yellow so that he made the wrong shade of green. what is the smallest amount of this green paint that he must throw away so that, using the rest of his green paint, and some extra blue or yellow paint he could make 5 liters of paint of the correct shade of green?
Found 2 solutions by ikleyn, greenestamps: Answer by ikleyn(49446) (Show Source):
You can put this solution on YOUR website!
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a painter wanted to mix 2 liters of blue paint with 3 liters of yellow paint to make 5 liters of green paint.
however, by mistake, he used 3 liters of blue and 2 liters of yellow so that he made the wrong shade of green.
what is the smallest amount of this green paint that he must throw away so that,
using the rest of his green paint, and some extra blue or yellow paint he could make 5 liters of paint
of the correct shade of green?
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After first (mistaken) mix, the painter has too much blue paint and too little yellow paint in the mixture, so, OBVIOUSLY, he should add extra yellow paint at some moment. After first (mistaken) mix, the painter has 5 liters of paint with 2 liters of yellow paint in it, which contents is 40% = 0.4 of yellow in the total of 5L volume. He poors out an unknown amount of V liters of the mixed paint and adds V liters of yellow paint. After it, the painter has 0.4*(5-V)+V liters of yellow paints in the 5 liters total volume. He wants the ratio be = 0.6, i.e. 0.4*(5-V) + V = 0.6*5. Simplify and find V 2 - 0.4V + V = 3 -0.4V + V = 3 - 2 0.6V = 1 V = 1/0.6 = = = liters. ANSWER. = 1.666. liters of the original mistaken mixture should be poored out and replaced with = 1.666. liters of yellow paint.
Answer by greenestamps(12280) (Show Source):
Here is a non-standard method for solving this kind of problem. Compare it to the standard solution shown by the other tutor and see if this method “works” for you.
When we get past all the words in the problem, we see that essentially the problem is mixing some paint that is 2/5 yellow with paint that is all yellow to get paint that is 3/5 yellow.
(1) Look at the three fractions of yellow on a number line — 2/5, 3/5, and 1 (=5/5).
(2) Observe/calculate that 3/5 is 1/3 of the way from 2/5 to 1.
(3) That means 1/3 of the mixture needs to be the all yellow paint.
(4) The mixture is to be 5 liters, so the amount of all yellow paint in the mixture should be 1/3 of 5 liters, which is 5/3 liters.
ANSWER: 5/3 liters, or 1 2/3 liters, of the original mixture should be thrown away and replaced with yellow paint to get the right shade of green.
Color Decoded: Stories That Span The Spectrum
That spectrum is red, orange, yellow, green, blue, and violet — no indigo. A pigment is a material that absorbs certain parts of the color spectrum and reflects others.
Color Decoded: Stories That Span The Spectrum
In this case the material — “YInMn blue,” named after its chemical makeup of yttrium, indium and manganese oxides — absorbed red and green wavelengths and reflected blue wavelengths in such a way that it came off looking a very bright blue.
Now, this particular blue is considered a “complex inorganic pigment.”
According to Geoffrey Peake, R&D manager at The Shepherd Color Co., that means it’s not a naturally occurring pigment (such as ultramarine, which comes from the rock lapis lazuli). Rather, it derives from a mix of various metal oxides — a metal element combined with oxygen.
“In our systems, blue is one of the most highly requested color families,” says Brooks Tippett, vice president of operations at the Pantone color company.
Blue — lonely, holy, hip, irreverent blue. It was the first man-made pigment, and the last color word developed across cultures.
The reason for both the above is that blue pigments are difficult and expensive to extract from nature. Lapis lazuli, for one, is mined mostly in Afghanistan and Pakistan. So synthetic pigments are easier to manufacture in bulk, and much more durable.
The last new complex inorganic blue pigment to be commercially manufactured was cobalt blue — a mix of cobalt and aluminum oxides — in the early 19th century. Cobalt, however, can be toxic if ingested in large quantities, and it doesn’t reflect heat particularly well. It fades over time.
Those aren’t terrible downsides, as colors go. But if a better one happens to fall into their laps?
Blue pigment discovered at Mas Subramanian’s lab at Oregon State University. Oregon State University hide caption
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Oregon State University
Blue pigment discovered at Mas Subramanian’s lab at Oregon State University.
Oregon State University
Blue is the coolest color
Subramanian and Smith, along with OSU chemistry professor Arthur Sleight, filed to patent the YInMn material before publishing a paper on their discovery with other collaborators in the Journal of the American Chemical Society.
Soon after, Peake says, Shepherd Color contacted OSU about testing out the pigment.
“I know from my experience — there will be a potential for commercialization,” Subramanian says.
Shepherd, unlike a company like Pantone, isn’t concerned with fashion, art, or other personal uses. It deals with paints and plastics that are made to be durable, used for outdoor applications like roofing and siding.
“It’s not like Joe Artist can call us up,” Peake says.
(That’s why the blue isn’t called anything more exciting than YInMn yet. When you’re an industrial manufacturer, Peake says, “it doesn’t seem necessary to have a catchier name.”)
Shepherd looks for four main things in a new pigment, Peake says: Is it a stronger color than what’s already available? Can it withstand elements like weather and heat? Are there cost advantages? And will they encounter any regulatory or environmental issues?
Shots – Health News
The sample order area at The Shepherd Color Co. in Cincinnati, where customers can request samples for their various products. Shepherd Color Co. hide caption
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Shepherd Color Co.
The sample order area at The Shepherd Color Co. in Cincinnati, where customers can request samples for their various products.
Shepherd Color Co.
“Immediately they said this was really an exceptional blue, because it reflects heat more than cobalt blue, it’s really stable and it’s a really great color like lapis lazuli,” Subramanian says.
Shepherd’s tests — turning it into paints and plastics, using it on ceramics and metals — also showed YInMn can endure oil, water and sunlight better than other available blues.
Once the Environmental Protection Agency approves YInMn for commercial manufacturing, Shepherd can begin selling it to other companies. For every kilogram of the pigment the company sells, Peake says, Shepherd pays a royalty to OSU.
Think of this like a record deal. Subramanian’s team and OSU wrote and own the tune, but Shepherd will market and distribute it — they’ll try to make it a hit. And a new hit in the color industry is a rare thing.
“I’ve been doing this job for 27 years, and maybe worldwide there have been five or six new inorganic pigments that have been commercialized over that time period,” Peake says.
A broader palette
Not that people aren’t always searching for more color.
Peake says Shepherd has a research and development lab that works methodically to invent new pigment chemistries. In 2012, it introduced NTP Yellow, which the company patented and now sells.
Subramanian’s current project includes a search for a better red pigment, which would be in high demand if found. Red tends to come from heavy metals or other toxic substances, like mercury and lead.
And Pantone — famous for its Color of the Year contest — regularly releases new shades into its standardized color systems. But according to Tippett, the Pantone vice president, those are primarily aimed at designers and the fashion and interiors industries, and based off a common, small group of pigments.
