Final Answer:
The correct inequality to find x, the minimum number of trophies, is D) 3.5x + 25 < 7.5x + 17.
Step-by-step explanation:
Veronica needs to determine the minimum number of trophies, represented by x, to ensure that the total cost at Company P is less than the total cost at Company R. Let's break down the costs for each company. Company P charges $3.50 for each trophy and has a one-time engraving fee of $25. So, the total cost at Company P is given by the expression 3.5x + 25. On the other hand, Company R charges $7.50 for each trophy and has a one-time engraving fee of $17. The total cost at Company R is represented by 7.5x + 17.
To set up the inequality, we compare the total costs, making sure the total cost at Company P is less than the total cost at Company R. This leads to the inequality 3.5x + 25 < 7.5x + 17. Now, we can simplify the inequality by subtracting 3.5x from both sides and subtracting 17 from both sides. This simplifies to 25 < 4x, and dividing both sides by 4 gives x > 6.25. Therefore, the minimum number of trophies, x, should be greater than 6.25 for the total cost at Company P to be less than the total cost at Company R.
In summary, the inequality 3.5x + 25 < 7.5x + 17 ensures that Veronica orders a minimum number of trophies, x, where the total charges at Company P are less than the total charges at Company R. The correct inequality to find x, the minimum number of trophies, is D) 3.5x + 25 < 7.5x + 17.