Certainly! Let's break down the problem step by step to see which value could replace [tex]\( x \)[/tex] in the table.
1. Identify Variables:
- Let [tex]\( h \)[/tex] be the number of hard cover books.
- The total number of books is 45.
- Therefore, the number of paperback books is [tex]\( 45 - h \)[/tex].
2. Weight Equations:
- The weight of one hard cover book is 7 ounces.
- The weight of one paperback book is 5 ounces.
- Let [tex]\( x \)[/tex] be the total weight of the paperback books.
3. Total Weight Calculation:
- The total weight of all 45 books is given as 249 ounces.
4. Equation for Total Weight:
- The total weight of the hard cover books is [tex]\( 7h \)[/tex] ounces.
- The total weight of the paperback books is [tex]\( 5(45 - h) \)[/tex] ounces.
- The combined total weight is 249 ounces.
5. Formulating the Equation:
[tex]\[
7h + 5(45 - h) = 249
\][/tex]
6. Solving for [tex]\( x \)[/tex]:
- Simplify the equation:
[tex]\[
7h + 5(45 - h) = 249
\][/tex]
[tex]\[
7h + 225 - 5h = 249
\][/tex]
[tex]\[
2h + 225 = 249
\][/tex]
[tex]\[
2h = 249 - 225
\][/tex]
[tex]\[
2h = 24
\][/tex]
[tex]\[
h = 12
\][/tex]
7. Calculating the Weight of Paperback Books:
- Substitute [tex]\( h = 12 \)[/tex] back into the expression for the weight of the paperback books:
[tex]\[
x = 5(45 - h)
\][/tex]
[tex]\[
x = 5(45 - 12)
\][/tex]
[tex]\[
x = 5(33)
\][/tex]
[tex]\[
x = 165
\][/tex]
8. Identify the Correct Value:
- Therefore, the value that could replace [tex]\( x \)[/tex] in the table is [tex]\[
5(45 - h)
\][/tex]
So, the correct value to replace [tex]\( x \)[/tex] in the table is [tex]\( 5(45 - h) \)[/tex].
