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The hardcover version of a book weighs 7 ounces while its paperback version weighs 5 ounces. Forty-five copies of the book weigh a total of 249 ounces.

[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
\multicolumn{4}{|c|}{Weight of Books} \\
\hline
& Number of Books & Weight per book (ounces) & Total Weight (ounces) \\
\hline
Hardcover & \(h\) & 7 & \(7h\) \\
\hline
Paperback & \(45 - h\) & 5 & \(x\) \\
\hline
Total & 45 & & 249 \\
\hline
\end{tabular}
\][/tex]

Which value could replace [tex]\(x\)[/tex] in the table?

A. [tex]\(40 - h\)[/tex]

B. [tex]\(50 - h\)[/tex]

C. [tex]\(5(45) - h\)[/tex]

D. [tex]\(5(45 - h)\)[/tex]

Sagot :

GinnyAnswer
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].
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