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There are 158 students registered for American History classes. There are twice as many students registered in second period as first period. There are 10 less than three times as many students in third period as in first period. How many students are in each period?

 Jan 23, 2020
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You'll want to express the number of students in each of the periods as a function of the number of students in a reference period.

Let x be first period, y second periodand z third period

We know what y=2x and z=3x-10

 and x+y+z=158 

Which you can then rewrite as a function of X 

x+2x+3x-10=158

6x-10=158

6x=158+10

x=168/6

x=28

y=2*28

z=28*3-10

 

So first semester 28 students, second semester 56 students and third semester 74 students.

 

Cheers

 Jan 23, 2020

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