This is a reuploaded question because i put the wrong symbol in. (ex, <, >)

Mr. Barkley's solutions are wrong!
Determine the error which was made. Please be specific!
In what step was the error?
What was done incorrectly?
What should have been done instead?
Solve the problem correctly.

Thelma has $178 in gift cards at the local hardware store. She plans to use them to buy a new set of wrenches and some welding rods. The wrench set costs $80. The welding rods are $10 per packet. What is the most number of packets of welding rods she will be able to buy?

Mr. Barkley's solution:
Let w = number of packets of welding rods.
100 + 10w ≤ 178
10w ≤ 78
w ≤ 7.8
7.8 rounds to 8.
Solution: Thelma can buy at most 8 packets of welding rods.

(This is a repost because I typed the question in wrong, thanks for helping anyway!)

Don't know where the $100 comes from, anyway ....

should be:
80 + 10w ≤ 178
10w ≤ 98
w ≤ 9.8

He can buy 9 welding rods to stay less than 178
If you round up to 10, he won't have enough money : 80 + 10*10 = 180