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
x = 28
Substitute x = 28 in eqn 2
y = 2(28)
y = 56
Substitute x = 28 in eqn 3
z = 3(28) - 10
z = 84 - 10
z = 74
Thus there are 28 students in first period and 56 students in sceond period and 74 students in third period