Let's solve the problem step by step.
1. Identify Known Variables and Values:
- The cost of one long-sleeved T-shirt is \[tex]$14.
- The cost of one short-sleeved T-shirt is \$[/tex]10.
- The total revenue from selling both types of T-shirts is less than \[tex]$200.
2. Form the Inequality Based on Costs:
- Let \( x \) be the number of long-sleeved T-shirts sold.
- Let \( y \) be the number of short-sleeved T-shirts sold.
3. Constructing the Inequality:
- The revenue generated from selling \( x \) long-sleeved T-shirts is \( 14x \) dollars.
- The revenue generated from selling \( y \) short-sleeved T-shirts is \( 10y \) dollars.
- The total revenue is the sum of these two amounts: \( 14x + 10y \).
4. Define the Total Revenue Constraint:
- We know that the total revenue is less than \$[/tex]200. This gives us the inequality:
[tex]\[
14x + 10y < 200
\][/tex]
Thus, the inequality that best represents the number of long-sleeved T-shirts [tex]\( x \)[/tex] and the number of short-sleeved T-shirts [tex]\( y \)[/tex] they have sold is:
[tex]\( 14x + 10y < 200 \)[/tex]
Therefore, the correct choice is:
4. [tex]\( 14x + 10y < 200 \)[/tex]
