SOLUTION: 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

Algebra ->  Expressions-with-variables -> SOLUTION: 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       Log On


   

Question 50052: 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?
Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the libaray books, y be the textbooks and z be the telephone books
EQUATION 1:
x+y+z=36
EQUATION 2:
x+z=2y ---> y=%28x%2Bz%29%2F2
EQUATION 3:
y+z=3x

SUb EQUATION 2 into 1 and 3
x%2B%28x%2Bz%29%2F2%2Bz=36
3x+3z=72 (EQUATION 4)

%28x%2Bz%29%2F2%2Bz=3x
x%2B3z=6x
3z-5x=0 (EQUATION 5)

Subtract equation4 from 5 and simplfy:
3x-(-5x)=72
3x+5x=72
8x=72
x=9

3z=5x
3z=5(9)
z=15

y=(x+z)/2
y=12
so hence, there are 9 libaray books, 12 textbooks and 15 telephone books in the locker.
Paul.