Help with the color of a star cluster

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In summary, the conversation is about finding the B-V magnitude of a star cluster with given numbers of F and M type stars and corresponding B-V values. The person has derived a formula for calculating the cluster's magnitude, but when using B-V values, the result is inaccurate. They tried averaging the luminosities and taking the difference of the two stellar types' B-V color, but the answer is still not accurate. They question if they are missing a basic concept and ask for help in calculating the B-V of the cluster.
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Astrofun42
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TL;DR Summary
Trying to calculate color of cluster from given distribution of stars, can't seem to get it right.
I am working on a problem which asks for the B-V magnitude of a star cluster given N stars of type F and M stars of type K. I have values for B-V for both stellar types. I've derived a general formula for computing the magnitude of the cluster from the magnitudes of each star type, which worked just fine for the first part of the problem (not shown here).

When I try to use the same formula for B-V values, I get an answer that is way off the mark. I then tried averaging the luminosities to get the luminosity of a 'typical' star in the B-V band, and what it's magnitude would be, and got closer to the answer, but not quite there.

Since B-V stands for mB - mV, I thought maybe the question is asking for the difference of the two stellar types' B-V color (subtracting one B-V from the other), which gave me the closest answer, but still .07 magnitude away. Am I missing a basic concept here?

What is the procedure for calculating the B-V of a cluster from the B-V of its constituent stars? Nowhere in the given data are there values for MB, so I'm at a loss. Thanks for any help.
 
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You need to show your work, e.g. the formula derived.
 

1. What is the color of a star cluster?

The color of a star cluster can vary depending on the age and composition of the stars within it. Generally, younger star clusters will appear blue or white, while older clusters will appear reddish or yellow.

2. How is the color of a star cluster determined?

The color of a star cluster is determined by the temperature of the stars within it. Hotter stars emit more blue light, while cooler stars emit more red light. The overall color of the cluster is a combination of the colors emitted by all the stars within it.

3. Can the color of a star cluster change over time?

Yes, the color of a star cluster can change over time as the stars within it age and evolve. As stars go through different stages of their life cycle, their temperature and color can change, affecting the overall color of the cluster.

4. How do scientists use the color of a star cluster to study it?

Scientists use the color of a star cluster to determine its age, composition, and distance from Earth. By analyzing the colors of the stars within the cluster, scientists can also make predictions about the future evolution of the cluster.

5. Can the color of a star cluster tell us anything about its size?

Yes, the color of a star cluster can give us some information about its size. Generally, larger star clusters will have a wider range of colors, as they contain stars of different ages and temperatures. Smaller clusters may have a more uniform color, indicating a more similar age and composition of stars.

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