To solve this problem, we need to determine the possible labor costs for repairing the bike, given that the total cost (parts and labor) will not exceed \[tex]$40. The parts themselves cost \$[/tex]17.50.
Let's denote the labor cost by [tex]\( L \)[/tex].
Given:
- Cost of parts = \[tex]$17.50
- Total maximum cost for parts and labor = \$[/tex]40
The parts and labor together should not be more than \$40, which gives us the following inequality:
[tex]\[ \text{Cost of parts} + \text{Labor cost} \leq \text{Total maximum cost} \][/tex]
[tex]\[ 17.50 + L \leq 40 \][/tex]
Therefore, the inequality showing the possible labor costs, [tex]\( L \)[/tex], is:
[tex]\[ 17.50 + L \leq 40 \][/tex]
Now, let's match this with the options provided:
A. [tex]\( 40 + 17.50 \geq L \)[/tex]
B. [tex]\( 40 + L \geq 17.50 \)[/tex]
C. [tex]\( 17.50 + L \leq 40 \)[/tex]
D. [tex]\( L - 17.50 \leq 40 \)[/tex]
The correct inequality, [tex]\( 17.50 + L \leq 40 \)[/tex], is option C.
