Question

Kyle is ready to place an order with Patty's Printing when he hears that a new company recently opened in town. Sherman's Shirts charges $20 to create the artwork for the team logo plus $8 per jersey. Which company has a lower total cost for different numbers of jerseys?
Drag each number of possible jerseys to the correct box to show whether one company has a lower total cost or the same total cost as the other company.
Lower total cost at Patty's Printing
Lower total cost at Sherman's Shirts
Same total cost at both companies
<
1
2
3
4
>
8
13
3 ::10
::12
:18

Answer 1

I’m missing Patty’s pricing. What does Patty’s Printing charge (fixed fee and/or per-jersey price)? Once you give that I’ll sort the jersey counts into the three boxes.

If it helps, here’s how I’ll do it and an example:

- Sherman's total cost = 20 + 8n (n = number of jerseys).
- If Patty’s cost = A + Bn, compare A + Bn to 20 + 8n:
- If A + Bn < 20 + 8n then Patty’s is cheaper.
- If A + Bn = 20 + 8n then they cost the same.
- If A + Bn > 20 + 8n then Sherman’s is cheaper.
- Solve equality A + Bn = 20 + 8n to find the break-even n: n = (20 − A) / (B − 8) (if B ≠ 8).

Example (if Patty’s had no setup fee and charged $10 per jersey):
- Patty’s = 10n, Sherman’s = 20 + 8n.
- 10n < 20 + 8n → 2n < 20 → n < 10 → Patty’s cheaper for n = 1,2,3,4,8.
- 10n = 20 + 8n → n = 10 → same at n = 10.
- 10n > 20 + 8n → n > 10 → Sherman’s cheaper for n = 12,13,18, etc.

Tell me Patty’s pricing (or confirm whether Patty’s is $10/jersey with no fee), and I’ll place the given numbers into the correct boxes.