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's break down the problem step-by-step.
Step 1: Assign variables to represent the unknowns.
Let's assume:
Number of library books = L
Number of textbooks = T
Number of telephone books = B
Step 2: Translate the given information into equations.
The problem states:
1) L + T + B = 36 (Total number of books in Kyle's locker)
2) L + T = 2T (The number of library books and textbooks combined equals twice the number of textbooks)
3) T + B = 3L (The number of textbooks and telephone books combined equals three times the number of library books)
Step 3: Simplify the equations.
From equation 2, we can rewrite it as:
L = T (Subtract T from both sides)
From equation 3, we can rewrite it as:
B = 3L - T (Subtract T from both sides)
Step 4: Substitute the simplified equations into the original equation.
Plug the simplified equations into the first equation:
L + T + B = 36
(T) + T + (3L - T) = 36 (Replace L with T and B with 3L - T)
4T + 3L = 36
Step 5: Solve the system of equations.
Now we have two equations:
4T + 3L = 36 (Equation from step 4)
L = T (Equation from step 3)
We can substitute the value of L from the second equation into the first equation:
4T + 3(T) = 36
4T + 3T = 36
7T = 36
T = 36/7
Step 6: Calculate the values.
Now that we have the value of T, we can substitute it into the second equation to find the value of L:
L = T = 36/7
Substituting T into the third equation to find the value of B:
B = 3L - T = 3(36/7) - 36/7
Step 7: Simplify the values.
Calculate the values of L, T, and B:
L = 36/7
T = 36/7
B = (3*36)/7 - (36/7)
Step 8: Convert the fractions into mixed numbers or decimals.
Simplifying the values:
L ≈ 5.14 (rounded to two decimal places)
T ≈ 5.14 (rounded to two decimal places)
B ≈ 17.71 (rounded to two decimal places)
Since we cannot have a fraction of a book, we can adjust the values to the nearest whole number:
L = 5
T = 5
B = 18
Therefore, there were 5 library books, 5 textbooks, and 18 telephone books in Kyle's locker.
To solve this problem, let's create a chart to better organize the given information and find a rule to determine the number of each type of book Kyle had in his locker.
Let "L" represent the number of library books, "T" represent the number of textbooks, and "B" represent the number of telephone books.
Based on the given information:
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 + B = 3L
Now, let's solve these two equations to find the values of L, T, and B.
From equation 1, we have: L + T = 2T
By subtracting T from both sides: L = T
Now, substitute L = T into equation 2: T + B = 3L
Replace L with T: T + B = 3T
Subtract T from both sides: B = 2T
We know that Kyle had a total of 36 books in his locker, so we can write another equation:
L + T + B = 36
Substitute L = T and B = 2T into this equation:
T + T + 2T = 36
4T = 36
T = 36/4
T = 9
Now that we found the value of T, we can find the values of L and B:
L = T = 9
B = 2T = 2 * 9 = 18
Therefore, Kyle had 9 library books, 9 textbooks, and 18 telephone books in his locker.