Liliana buys some softballs at [tex]$\$[/tex] 3[tex]$ each and gloves at $[/tex]\[tex]$ 20$[/tex] each for her PE class. She buys twice as many balls as gloves. She spends [tex]$\$[/tex] 138[tex]$ in total, which includes $[/tex]\[tex]$ 8$[/tex] tax. Which equation would you use to find the number of gloves she buys?

Let [tex]$x$[/tex] represent the number of gloves she buys.
A. [tex]$20(2x) + 3(x) + 8 = 138$[/tex]
B. [tex]$x + 2x + 8 = 138$[/tex]
C. [tex]$20(x) + 3(2x) + 8 = 138$[/tex]
D. [tex]$20(x) + 3(2x) = 138$[/tex]



Answer :

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.