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

let ..

number of textbooks be x
number of library books by y
number of telephone books by z

x+y+z = 36 (#1)

y+x = 2x --- > y = x (#2)

x+z = 3y --- z = 3y - x (#3)

back in #1
x+y+z = 36
x + x + (3y-x) = 36
x+x+(3x-x) = 36
4x=36
x=9
then y=9
z = 18

9 library books
9 textbooks
18 telephone books

To solve this problem, we can create a chart to keep track of the given information. Let's assign variables to represent the number of library books (L), textbooks (T), and telephone books (P).

According to the problem, we know that:
1. L + T + P = 36 (The total number of books is 36)
2. L + T = 2T (The number of library books and textbooks combined equals twice the number of textbooks)
3. T + P = 3L (The number of textbooks and telephone books combined equals three times the number of library books)

Now, let's use the chart to find the solution step by step:

| Type of Books | Number of Books |
|:-----------------:|:--------------:|
| Library Books | L |
| Textbooks | T |
| Telephone Books | P |

From equation 2 (L + T = 2T), we can simplify it to L = T.

Let's substitute L with T in equation 3. We get T + P = 3(T).
Expanding the equation gives us T + P = 3T.

We can simplify this equation as 2T = P, which means the number of textbooks is double the number of telephone books.

Using the values we have, we can substitute T with P/2 in equation 1.
T + P/2 + P = 36
Combining like terms, we get 3T/2 + P = 36
Multiplying both sides by 2, we get 3T + 2P = 72.

Now, substitute T with P/2 in equation 3.
P/2 + P = 3L
Combining like terms, we get 3P/2 = 3L
Dividing both sides by 3, we get P/2 = L

From these equations, we can see that T = P/2, P/2 = L.

Now, let's substitute P/2 for T in equation 1.
L + P/2 + P = 36
Combining like terms, we get L + (3P/2) = 36
Adding (3P/2) to both sides, we get L = 36 - (3P/2)
Simplifying further, we get L = (72 - 3P)/2

Now let's substitute P/2 for L in equation 2.
P/2 + T = 2T
Replacing L with P/2, we get P/2 + T = 2T
Subtracting T from both sides, we get P/2 = T

From these equations, we can conclude that T = P/2 and L = (72 - 3P)/2.

To find the values of L, T, and P, we need to find a combination of P that satisfies these equations and fits within the given constraints.

Let's try different values of P (the number of telephone books), plug them into the equations, and see if we get valid solutions:

For P = 2,
L = (72 - 3(2))/2 = (72 - 6)/2 = 66/2 = 33
T = 2/2 = 1

For P = 4,
L = (72 - 3(4))/2 = (72 - 12)/2 = 60/2 = 30
T = 4/2 = 2

For P = 6,
L = (72 - 3(6))/2 = (72 - 18)/2 = 54/2 = 27
T = 6/2 = 3

From these calculations, we can see that the combination of 33 library books, 1 textbook, and 2 telephone books satisfies all the given conditions.

So, the answer is:
Kyle had 33 library books, 1 textbook, and 2 telephone books in his locker.