Brain Teaser......?

I'm having problems with this math problem.....Kyle had 36 books in his locker. Some were library books, some were textbooks, and the rest were telephone books. The number of library books and telephone books combined equals twice the number of textbooks. The number of textbooks and telephone books combined equals three times the number of library books. How many of each type of book were in Kyle's locker?

Can you please help? And can you tell me how you got it, too? Also, if you know the answer but don't know how to work it, just tell me the answers. Thanks! =)

L = # of library books
T = # of text books
P = # of phone books

The first equation is obvious because Kyle has 36 books:

L + P + T = 36

You are told that library books (L) combined with phone books (P) equals twice the number of textbooks (2T)

L + P = 2T

With these two equations you can figure out the number of telephone books:

L + P + T = 36

Substitute in L + P = 2T
(2T) + T = 36
3T = 36
T = 12

The final statement is textbooks (T) plus phone books (P) equals three times the number of library books (3L)

T + P = 3L

Substitute T = 12
12 + P = 3L

Do the same in the prior equation:
L + P = 2T
L + P = 2(12)
L + P = 24

Solve for P:
P = 24 - L

Substitute into the equation above:
12 + (24-L) = 3L
12 + 24 - L = 3L
36 = 4L
9 = L

And the final one is easy to figure out.
T + L + P = 36
(12) + (9) + P = 36
21 + P = 36
P = 15

So Kyle has 9 library books, 12 text books and 15 phone books

Double-check:
9 + 12 + 15 = 36 check
9 + 15 = 2(12) check
12 + 15 = 3(9) check

is it 12?

x = number of library books
y = number of textbooks
z = number of telephone books

The number of library books and telephone books combined equals twice the number of textbooks.
x + z = 2y

number of textbooks and telephone books combined equals three times the number of library books
y + z = 3x

there are 36 books total
x + y + z = 36

now solve
x + z = 2y
x + z - 2y = 0

y + z = 3x
y + z - 3x = 0

x + z - 2y = 0
y + z - 3x = 0
x + y + z = 36


-1(x + z - 2y = 0)
y + z - 3x = 0

-x - z + 2y = 0
y + z - 3x = 0
-------------------
-4x + 3y = 0



y + z - 3x = 0
x + y + z = 36

-1(y + z - 3x = 0)
x + y + z = 36

-y - z + 3x = 0
x + y + z = 36
--------------------
4x = 36
x = 9

-4(9) + 3y = 0
3y = 36
y = 12

z = 36 - (12 + 9)
z = 15


9 library books
12 text books
15 telephone books

l=library p=phone t=text

t+p+l = 36
l+p=2t
t+p=3l

rearrange the first one so t+p = 36-l

sub that in to the 3rd equation so 36-l = 3l and you get l=9
sub 9 into the second eqation to get p=2t-9. sub p and l into the 3rd equation to get t + 2t-9 = 3(9) which solves to t=12

which leaves p=15

36 = L + T + P This is the basic formula
L is library books
T is textbooks
P is phonebooks
36 is the total number of books
2T = L + P library books and phone books equals twice the textbooks
3L = T + P text and phone books are equal to 3 times the library books

start with one equation like 2T = L + P but get 2T to other side
0 = - L- P + 2T multiply both sides by -1 to create a situation where you can take another equation and solve it for one variable by eliminating the others like:
36 = L+ P + T
0 = -L - P +2T
36 = 3T
12 = T now you know what T is
solve another variable doing the same:
0 = -3L + P +T moved 3L to the other side
-36 = -L - P - T multiplied both sides by -1
-36 = -4L eliminated P and T
9 = L
If L is 9 and T is 12 then 36 - L -T = P
PHONE BOOKS = 15

substitute numbers in equations to prove answers:

T + P = 3L
12 + 15 = 3 * 9
27 = 27 True

L + P = 2 * T
9 + 15 = 2 * 12
24 = 24 True

36 = L + T + P
36 = 9 + 12 + 15
36 = 36 true - must be good answer