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?

There are 28 students in first period and 56 students in sceond period and 74 students in third period

Solution:

Let the number of students in first period be "x"

Let the number of students in second period be "y"

Let the number of students in third period be "z"

There are 158 students registered for American History classes.

Therefore,

x + y + z = 158 eqn 1

There are twice as many students registered in second period as first period

number of students in second period = twice of number of students in first period

y = 2x eqn 2

There are 10 less than three times as many students in third period as in first period

number of students in third period = 3 times number of students in first period - 10

z = 3x - 10 eqn 3

Substitute eqn 2 and eqn 3 in eqn 1

x + 2x + 3x - 10 = 158

6x = 168

Substitute x = 28 in eqn 2

y = 2(28)

Substitute x = 28 in eqn 3

z = 3(28) - 10

z = 84 - 10

Thus there are 28 students in first period and 56 students in sceond period and 74 students in third period

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