Let's analyze each statement in the context of the equation [tex]\(8l + 5s = 128\)[/tex], which represents this week's earnings from puzzle sales, where [tex]\(l\)[/tex] represents the number of large puzzles sold and [tex]\(s\)[/tex] represents the number of small puzzles sold.
### Analyzing the Coefficients
1. The coefficient 8 in the equation gives the cost of one small puzzle.
- This statement is incorrect. The coefficient 8 corresponds to the cost of one large puzzle. From the given information, 2 large puzzles are sold for [tex]$16, meaning one large puzzle costs \(\$[/tex]16 / 2 = \[tex]$8\).
2. The coefficient 5 in the equation gives the cost of one large puzzle.
- This statement is incorrect. The coefficient 5 corresponds to the cost of one small puzzle. Since 3 small puzzles are sold for $[/tex]15, the cost of one small puzzle is [tex]\(\$15 / 3 = \$5\)[/tex].
3. The constant 128 in the equation gives the total number of puzzles sold.
- This statement is incorrect. The constant 128 in the equation represents the total amount of money earned from puzzle sales, not the number of puzzles sold.
4. The coefficient 8 in the equation gives the cost of one large puzzle.
- This statement is correct. As determined earlier, one large puzzle costs [tex]$8.
5. The coefficient 5 in the equation gives the cost of one small puzzle.
- This statement is correct. As determined earlier, one small puzzle costs $[/tex]5.
### Summary of Correct Statements
Based on the analysis, the correct statements are:
- The coefficient 8 in the equation gives the cost of one large puzzle.
- The coefficient 5 in the equation gives the cost of one small puzzle.
In conclusion, the correct statements regarding the equation [tex]\(8l + 5s = 128\)[/tex] are:
- The coefficient 8 in the equation gives the cost of one large puzzle.
- The coefficient 5 in the equation gives the cost of one small puzzle.
