kyle had 36 books in hislocker. some were library books, some were textbooks, and the rest were telophone books. the number of library books and textbooks combined equal 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??

please help me....i need a chart or a rule to show me how u got it....please

Do it this way

a=library books
b=textbooks
c=telephone books

You know a + b + c = 36
You know that a + b = 2b (library books plus textbooks equals twice number of textbooks)
You know that b + c = 3a (textbooks plus telephone books equals three times number of library books)

Take equation #2 a+b=2b
Subtract b from each side
a=b The number of library books equals the number of textbooks

Take equation #3 b+c=3a Substitute a for b since you know now from equation #2 that a=b Now you have a+c=3a
Subtract a from each side c=2a

Now, go to equation #1 a+b+c=36

You know a=b
You know c=2a
substitute
a + a + 2a = 36

Combine like terms and divide
4a = 36 a= 9

Again, you know a = b and c= 2a therefore a=9, b=9, c=18
9 library books
9 text books
18 telephone books

b= Library

t= Textbooks
p= Telephone

1) b+p= 2t
2) t+p= 3b
3) b+t+p= 36

Let's use the information provided to solve the problem step by step.

Let's represent the number of library books as L, the number of textbooks as T, and the number of telephone books as P.

From the given information, we can set up the following equations:

Equation 1: L + T + P = 36 (since Kyle had a total of 36 books)

Equation 2: L + T = 2T (the number of library books and textbooks combined equal twice the number of textbooks)

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

Now let's solve the equations step by step:

1. From Equation 2: L + T = 2T, we can rewrite it as L = T. (subtract T from both sides)
Substitute this value into Equation 3.

Equation 3 becomes: T + P = 3(T)

2. From Equation 3: T + P = 3T, we can rewrite it as P = 2T. (subtract T from both sides)

3. Now substitute the values of L and P into Equation 1.

L + T + P = 36
T + T + 2T = 36
4T = 36
T = 36/4
T = 9

4. Now substitute the value of T into Equation 2 to find the value of L.

L = T
L = 9

5. Substitute the value of T into Equation 3 to find the value of P.

P = 2T
P = 2(9)
P = 18

So, the solution is L = 9 library books, T = 9 textbooks, and P = 18 telephone books.

Here's a chart to summarize the results:

Type of Book | Number of Books
------------------------------
Library Books | 9
Textbooks | 9
Telephone Books | 18

I hope this helps! Let me know if you have any further questions.

To solve this problem, let's create a table to keep track of the given information and use variables to represent the unknown quantities.

Let's use the following variables:
L = number of library books
T = number of textbooks
P = number of telephone books

According to the problem:
1. The number of library books and textbooks combined equals twice the number of textbooks.
L + T = 2T

2. The number of textbooks and telephone books combined equals three times the number of library books.
T + P = 3L

Now let's solve this system by substitution or elimination method.

Method 1: Substitution Method
Using equation 1, we can express L in terms of T:
L = 2T - T
L = T

By substituting L = T into equation 2, we get:
T + P = 3(T)
T + P = 3T

Now, let's solve for P in terms of T:
P = 3T - T
P = 2T

So, we have:
L = T
P = 2T

Since the problem states that Kyle had 36 books in total, we can write:
L + T + P = 36

Substituting the values we found, we get:
T + T + 2T = 36
4T = 36
T = 9

Substituting T = 9 into our equations, we find:
L = 9
P = 2(9) = 18

Therefore, Kyle had:
9 library books, 9 textbooks, and 18 telephone books in his locker.