MEghan had 36 books in her locker. Some were library books, text books and the rest were telephone books. THe number of library books and phone books combined equals twice the number of text books. The number of text books and telephone books equals three times the number of library books. How many of each kind of book were in Megan's locker?

telephone books --- x

textbooks ----- y
library books 36-x-y

36-x-y + x = 2y or 3y = 36
y = 12
y + x = 3(36-x-y)
y+x = 108 - 3x - 3y
4x + 4y = 108
x+y= 27
but y = 12
so, x + 12 = 27
x = 15
then 36-12-15 = 9

number of telephone books = 15
number of textbooks = 12
number of library books = 9

gajkwh;reg

To solve this problem, let's assign variables to represent the unknowns. Let:

- L = the number of library books
- T = the number of text books
- P = the number of telephone books

Based on the given information, we can set up a system of equations:

1) L + T + P = 36 (Equation 1: The total number of books is 36)

2) L + P = 2T (Equation 2: The number of library and telephone books combined equals twice the number of text books)

3) T + P = 3L (Equation 3: The number of text and telephone books equals three times the number of library books)

Now, let's solve this system of equations.

We can start by manipulating Equation 3 to express P in terms of L and T:
T + P = 3L
P = 3L - T (Equation 4)

Substitute Equation 4 into Equation 2:
L + (3L - T) = 2T
4L - T = 2T
4L = 3T
T = (4/3)L (Equation 5)

Now substitute Equation 5 into Equation 1:
L + (4/3)L + P = 36
(7/3)L + P = 36 (Equation 6)

Next, we need to express P in terms of L. Let's manipulate Equation 6:
(7/3)L + P = 36
P = 36 - (7/3)L (Equation 7)

We have now expressed both P and T in terms of L. Let's substitute Equations 5 and 7 into Equation 1:
L + T + P = 36
L + (4/3)L + (36 - (7/3)L) = 36
L + 4L/3 + 36 - 7L/3 = 36
(3L + 4L + 108 - 7L) / 3 = 36
(108 - L) / 3 = 36
108 - L = 108
L = 108 - 36
L = 72

Now that we know L = 72, we can plug this value back into Equation 5 to find T:
T = (4/3)L
T = (4/3)(72)
T = 96

Finally, we can substitute the values of L and T back into Equation 7 to find P:
P = 36 - (7/3)L
P = 36 - (7/3)(72)
P = 36 - (7/3)(24)
P = 36 - 56
P = -20

However, we cannot have a negative number of books. This suggests that there might be an error in the problem statement or in the calculations. Please double-check the information provided or let me know if there might be any other missing details in the problem.