Final answer:
The fewest number of medals that can be purchased from Company Y to have a lower total cost than Company Z is 9. This is calculated by comparing the total costs for both companies based on the number of medals and finding the point where Company Y becomes cheaper.
Step-by-step explanation:
We are asked to find the fewest number of medals that can be purchased from Company Y to have a lower total cost than Company Z. To do this, we set up two equations that represent the total cost (C) for each company based on the number of medals (m) purchased. For Company Y, the equation is C = 3.50m + 9.99, and for Company Z, the equation is C = 3.99m + 5.99. To find out when Company Y is cheaper, we look for the point where their total cost is less than Company Z's: 3.50m + 9.99 < 3.99m + 5.99
Subtract 3.50m from both sides: 9.99 < 0.49m + 5.99
Subtract 5.99 from both sides: 4.00 < 0.49m
Divide both sides by 0.49: m > 8.16
Since you can't purchase a fraction of a medal, round up to the next whole number. Therefore, the fewest number of medals that must be purchased from Company Y to have a lower total cost than Company Z is 9, which makes option A the correct answer.