To solve this problem, we need to examine the given equation and interpret what it represents. The equation given is:
[tex]\[ y = 11x + 25 \][/tex]
where [tex]\( y \)[/tex] is the total cost in dollars for printing [tex]\( x \)[/tex] custom t-shirts.
1. Understand the equation components:
- The slope (coefficient of [tex]\( x \)[/tex]) is [tex]\( 11 \)[/tex]. This means that for each additional t-shirt printed, the cost increases by [tex]\( 11 \)[/tex] dollars.
- The constant term [tex]\( 25 \)[/tex] is the fixed cost, which does not change regardless of the number of t-shirts printed.
2. Break down the impact of adding an additional t-shirt:
- The term [tex]\( 11x \)[/tex] indicates that every additional t-shirt adds [tex]\( 11 \)[/tex] dollars to the total cost.
- [tex]\( 25 \)[/tex] is a fixed cost that covers the initial setup or other fixed expenses and remains constant irrespective of how many t-shirts are printed.
From the structure of the equation [tex]\( y = 11x + 25 \)[/tex], it is clear the variable part, which is [tex]\( 11x \)[/tex], determines how the total cost changes with the number of t-shirts added.
3. Evaluate the statements:
- Statement A: "Each additional t-shirt being printed will increase the total cost by [tex]\( 11\% \)[/tex]". This statement is incorrect because the increase is a fixed amount, not a percentage.
- Statement B: "Each additional t-shirt being printed will increase the total cost by [tex]\( 25 \)[/tex] dollars". This is incorrect as the 25 dollars is a fixed initial cost, not the cost per additional t-shirt.
- Statement C: "Each additional t-shirt being printed will increase the total cost by [tex]\( 11 \)[/tex] dollars". This is correct as represented by the coefficient [tex]\( 11 \)[/tex] in the equation.
- Statement D: "Each additional t-shirt being printed will increase the total cost by [tex]\( 25\% \)[/tex]". This is incorrect as the percentage mentioned does not reflect the fixed increase per t-shirt, which is [tex]\( 11 \)[/tex] dollars.
Therefore, the correct statement is:
[tex]\[ \boxed{\text{C}} \][/tex]
