Let's approach this problem step-by-step:
1. Define the variables:
- Let [tex]\(x\)[/tex] represent the number of gloves Liliana buys.
2. Cost of the gloves:
- Each glove costs [tex]$\$[/tex] 20[tex]$, so the total cost for \(x\) gloves is \(20x\) dollars.
3. Number of softballs:
- Liliana buys twice as many softballs as gloves, meaning she buys \(2x\) softballs.
4. Cost of the softballs:
- Since each softball costs $[/tex]\[tex]$ 3$[/tex], the total cost for [tex]\(2x\)[/tex] softballs is [tex]\(3 \times 2x = 6x\)[/tex] dollars.
5. Incorporate the tax:
- There is an additional [tex]$\$[/tex] 8[tex]$ tax on the total purchase.
6. Total spending equation:
- The total amount spent, including the gloves, softballs, and tax, adds up to $[/tex]\[tex]$ 138$[/tex]. Therefore, the equation that represents the total expenditure is:
[tex]\[
20x + 6x + 8 = 138
\][/tex]
- Simplifying this equation:
[tex]\[
26x + 8 = 138
\][/tex]
Given the options, the correct equation that matches is:
C. [tex]\(20(x) + 3(2x) + 8 = 138\)[/tex].
[tex]\[
20(x) + 3(2x) + 8 = 138
\][/tex]
Hence, the correct answer is option C.
