Let's break down the given problem into steps to find the number of hardcover books [tex]\( h \)[/tex] and the correct value for [tex]\( x \)[/tex], which is the total weight of the paperback books.
### Step 1: Write Down the Information
We know from the problem statement:
- The weight of a hardcover book is 7 ounces.
- The weight of a paperback book is 5 ounces.
- There are 45 copies of the book.
- The total weight of the books is 249 ounces.
### Step 2: Define Variables
Let [tex]\( h \)[/tex] be the number of hardcover books. Consequently, the number of paperback books would be [tex]\( 45 - h \)[/tex].
### Step 3: Formulate the Equation
The total weight of the hardcover books and the paperback books combined equals the total weight of all books:
[tex]\[ 7h + 5(45 - h) = 249 \][/tex]
### Step 4: Solve the Equation for [tex]\( h \)[/tex]
First, distribute the 5 on the left-hand side:
[tex]\[ 7h + 225 - 5h = 249 \][/tex]
Combine like terms:
[tex]\[ 2h + 225 = 249 \][/tex]
Subtract 225 from both sides:
[tex]\[ 2h = 24 \][/tex]
Divide by 2:
[tex]\[ h = 12 \][/tex]
So, there are 12 hardcover books.
### Step 5: Calculate the Total Weight of Paperback Books
Since there are 12 hardcover books, the number of paperback books is:
[tex]\[ 45 - 12 = 33 \][/tex]
Then, the total weight of the paperback books is:
[tex]\[ 5 \times 33 = 165 \][/tex]
### Step 6: Identify the Correct Value of [tex]\( x \)[/tex]
The value of [tex]\( x \)[/tex] in the table represents the total weight of the paperback books. Therefore, the correct value of [tex]\( x \)[/tex] is:
[tex]\[ 5(45 - h) \][/tex]
Thus, the appropriate choice from the given options is:
[tex]\[ 5(45 - h) \][/tex]
### Conclusion
The correct value that could replace [tex]\( x \)[/tex] in the table is [tex]\( 5(45 - h) \)[/tex], and [tex]\( x \)[/tex] equals:
[tex]\[ 165 \][/tex]
Hence, the complete step-by-step solution confirms the value of [tex]\( x \)[/tex], which is the total weight of the paperback books.
