This is quite a multi-layered problem, so I am going to try my best to answer this in a way that makes sense. Compounding interest is basically "interest on interest," so any remaining balances have interest charged on them (in this case, 23.5% every month that there is a balance left on the card. I will bold any interests calculated and use that at the end.
First, let's calculate the remaining balance after the first month's payment of $175:
487.89 - 175 = 312.89
Then, we will calculate the new balance for the next month by calculating the 23.5% interest and then adding it to the total:
312.89 × 0.235 = 73.53 (rounded up)
312.89 + 73.53 = 386.42
Next, we will repeat the first step again:
386.42 - 175 = 211.42
Then, we will repeat step two again, and continue repeating steps 1 and 2 until the balance remaining is 0:
211.42 × 0.235 = 49.68
211.42 + 49.68 = 261.10
261.10 - 175 = 86.10
86.10 × 0.235 = 20.23
86.10 + 20.23 = 109.30
109.30 - 109.90 = 0.00 end balance.
Lastly, the question asks for how much Kayla pays in interest only, so all we need to do is add up the interest we calculated during the problem:
73.53 + 49.68 + 20.23 = $143.44
Looks like Kayla paid $143.44 in interest.
Hopefully I calculated this properly, so double check the math.