Your math supports what I've been telling him too. You applied for 15 jobs and got 1 interview. If that math held, you would need to apply for 150 jobs. But I think 100 is probably fine. Let us know what you're doing and I'm sure we can supply some suggestions.
Where are you getting your job leads? I was able to rustle up 265 possible companies for him to look into in about 2 hours after he told me there weren't even 100 places he could apply to. And I could have easily found 2x that but I got tired and petered out.
Something that tends to annoy me about these threads is when people (not you) emphatically declare their advice like it's The Truth when it's just want they do or sometimes it's just what they believe people should do and, even if it's true for their industry (which it isn't always), it's true for absolutely every one.
The best advice IMO comes from people who actually screen resumes and interview applicants and hire them because they are telling you what they actually do not what people wish they'd do.
As an example, I have read 100x that you should screen your resume for typos and spelling errors and that many employers will throw a resume out if it has even one typo in it. Now, I think it's good advice to proof-read your resume several times. Typos are embarrassing if they are noticed. (And speaking of the resume writer question that started this thread, one of my complaints with both the ones I used was that they *introduced* typos and grammatical errors into my resume that I then had to hunt down and fix.)
However, I can tell you that every resume I was given this year to look at prior to interviewing a candidate has typos and misspellings in them and that we not only interviewed those people, we hired some of them. Yes, it bugged the crap out of me. But it's the nature of my industry and the job I do that management doesn't care about those things even presuming they speak English well enough to even notice. It's also the nature of my industry that, if you threw out all the resumes with errors, you wouldn't have many to look at and you'd be throwing out some good candidates.
(That said, I gave the thumbs down to one that was so bad I felt like working with the person would be a nightmare because it would be impossible to communicate with them and I suspected their attention to detail was even more minimal than the people we already have.)