Answer :
To solve this problem, we need to determine how many copies of each type of paperback book were in the shipment. We know the total number of books and their combined weight, and we need to use this information to find out how many of each type of book are in the box.
Let's break it down step-by-step:
1. Define the Variables:
- Let [tex]\( x \)[/tex] represent the number of the first type of paperback books.
- Let [tex]\( y \)[/tex] represent the number of the second type of paperback books.
2. Set Up the Equations:
- We know the total number of books is 179. Therefore, the equation for this is:
[tex]\[
x + y = 179
\][/tex]
- We know the total weight of the books is 128 pounds. The first type of book weighs [tex]\(\frac{2}{3}\)[/tex] of a pound, and the second type weighs [tex]\(\frac{3}{4}\)[/tex] of a pound. Therefore, the equation for the weight is:
[tex]\[
\frac{2}{3}x + \frac{3}{4}y = 128
\][/tex]
3. Solve the Equations:
By solving these simultaneous equations, we can find the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex].
- From the given calculations:
- [tex]\( x = 75 \)[/tex] (number of the first type of paperback books)
- [tex]\( y = 104 \)[/tex] (number of the second type of paperback books)
4. Conclusion:
- There are 75 copies of the first type of paperback book.
- There are 104 copies of the second type of paperback book.
These results tell us how many of each type of book are in the shipment, based on the information provided about their total number and weight.
Let's break it down step-by-step:
1. Define the Variables:
- Let [tex]\( x \)[/tex] represent the number of the first type of paperback books.
- Let [tex]\( y \)[/tex] represent the number of the second type of paperback books.
2. Set Up the Equations:
- We know the total number of books is 179. Therefore, the equation for this is:
[tex]\[
x + y = 179
\][/tex]
- We know the total weight of the books is 128 pounds. The first type of book weighs [tex]\(\frac{2}{3}\)[/tex] of a pound, and the second type weighs [tex]\(\frac{3}{4}\)[/tex] of a pound. Therefore, the equation for the weight is:
[tex]\[
\frac{2}{3}x + \frac{3}{4}y = 128
\][/tex]
3. Solve the Equations:
By solving these simultaneous equations, we can find the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex].
- From the given calculations:
- [tex]\( x = 75 \)[/tex] (number of the first type of paperback books)
- [tex]\( y = 104 \)[/tex] (number of the second type of paperback books)
4. Conclusion:
- There are 75 copies of the first type of paperback book.
- There are 104 copies of the second type of paperback book.
These results tell us how many of each type of book are in the shipment, based on the information provided about their total number and weight.
