Step 1 :From Tuesday to Friday, Noel delivered 350 yards of ribbon per day for 4 days. So, the total length of ribbon delivered from Tuesday to Friday is \(350 \text{ yards/day} \times 4 \text{ days} = 1400 \text{ yards}\).
Step 2 :From Saturday to Monday, Noel delivered 700 yards of ribbon per day for 3 days. So, the total length of ribbon delivered from Saturday to Monday is \(700 \text{ yards/day} \times 3 \text{ days} = 2100 \text{ yards}\).
Step 3 :The total length of ribbon delivered from Tuesday to Monday is \(1400 \text{ yards} + 2100 \text{ yards} = 3500 \text{ yards}\).
Step 4 :The total number of days from Tuesday to Monday is 7 days.
Step 5 :So, the average length of ribbon that Noel delivered per day is \(\frac{3500 \text{ yards}}{7 \text{ days}}\).
Step 6 :Final Answer: The average length of ribbon that Noel delivered per day is \(\boxed{500} \text{ yards}\).