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The soccer team is conducting a fundraiser selling long-sleeved [tex]$T$[/tex]-shirts for [tex]$\$[/tex]14[tex]$ and short-sleeved $[/tex]T[tex]$-shirts for $[/tex]\[tex]$10$[/tex]. So far, the team has sold less than [tex]$\$[/tex]200[tex]$ worth of the two types of $[/tex]T[tex]$-shirts. Which inequality best represents $[/tex]x[tex]$, the number of long-sleeved $[/tex]T[tex]$-shirts they have sold, and $[/tex]y[tex]$, the number of short-sleeved $[/tex]T[tex]$-shirts they have sold?

A. $[/tex]x + y < 200[tex]$
B. $[/tex]x + y > 200[tex]$
C. $[/tex]14x + 10y > 200[tex]$
D. $[/tex]14x + 10y < 200$



Answer :

GinnyAnswer
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]