300 people joined the community orchestra. Some intended to play a string instrument, some a brass instrument, and the others percussion. If 3 times as many people were planning to play a string instrument as a brass instrument, and if 60 fewer were going to play percussion than a brass instrument, how many people were planning to play each type of instrument?

Question

Cayden

Mathematics

Today, 10:34

300 people joined the community orchestra. Some intended to play a string instrument, some a brass instrument, and the others percussion. If 3 times as many people were planning to play a string instrument as a brass instrument, and if 60 fewer were going to play percussion than a brass instrument, how many people were planning to play each type of instrument?

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Answers (1)

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Adelyn Stewart · Answer 1

Total amount of instrument players = 300

Number of brass instrument players = x (because we do not know how many there are, except that all other values that we must calculate are based off of the number of brass players we have

Number of string instruments = 3x (because 3 times more than the number of brass instruments

Number of Percussion = x-60 (because there are 60 less percussion players than brass players

So, our equation is (number of string instruments) + (number of brass instruments) + (number of percussion instruments) = 300 (which is our total possible number of people

3x+x+x-60=300

3x+x+x=360

5x=360

x = 72

We have 72 brass instrument players, 3 (72) = 216 string instrument players, and 72-60=12 percussion players

check: 72+216+12=300