A 'starry sky' that's installed on the roof is made with light fibers in a way, that the roof is surfaced with tiles that have been drilled with a proper number of fitting holes. The light fibers are installed into the holes before attaching the tiles.
Mike has been requested to make a starry sky roof, that uses a total of 200 light fibers. The work must be executed so that the roof has 3 different-sized 'stars' drilled into it by these rules:
-20% of the stars must be large, fitting 5 fibers each.
-35% of the stars must be medium, fitting 3 fibers each.
-Rest of the stars are small, each having 1 fiber fit into them.
a)How many holes must Mike drill in total?
b)How many holes are large, medium and small, respectively?
This one has been giving me a headache since I first encountered it. I'd appreciate to hear the reasoning behing the solution.
First we need to know the minimum number of stars. $$HCF(20\%,35\%,45\%)=5\%$$ Now, $$\frac{100\%}{5\%}=20$$ We need atleast $20$ stars to get an integral answer. For $20$ stars, we require a total of $(20\%\times20)\times5+(35\%\times20)\times3+(45\%\times20)\times1=50$ fibres.
Since we must use a total of $200$ fibres, we need to have $4$ times the number of stars and fibres. So we need a total of $80$ stars.