3 assumptions you made where this comes apart:
1. The 3 million shots a day includes people getting their second dose. You did not take that into account as you assumed all 105 million doses would go to first doses.
2. You have to leave enough time for the new people to get a second dose. 59-35=24 days remaining. You would have to administer 4.4 million doses daily just to cover that 105 million in that time period.
3. 158 million doses have been administered which includes people's second doses. 101.8 million people have received at least 1 dose and 58 million have been fully vaccinated. Reference:
https://covid.cdc.gov/covid-data-tracker/#vaccinations
More realistic math:
-43.8 million will get their second dose in the coming month, bringing 18+ vaccination percentage to 39.2%.
-3 million doses (higher than current but it is trending upward) will be administered per day, allowing 90 million doses over the next 30 days.
-90-43.8 gives us 46.2 million doses that are administered to first timers over that 30 day period.
-There are ~258 million people above the age of 18 who we plan to vaccinate.
-At the end of May we should have ~148 million people fully vaccinated and another 46.2 million that have received their first dose. 148/258 million gives us 57.3% of 18+ fully vaccinated and 194.2/258 gives us 75.2% of 18+ that have received at least one dose.
But what do I know, math isn't my strong point. I'm only an Engineer.
Math doesn't lie but it can lead you astray when your assumptions aren't good going in. Garbage in, garbage out.
The only mistake I made was in not factoring in the 60 millions under the age of 14. If you re read my post I used 5 weeks and specially mentioned that it leaves 3 weeks to get the second shot. When I mentioned 150 million people I stated had received at least one shot, meaning everyone who had gotten the shot at that time would get there second shot prior to 5/31. The reports I see show 3 million approx a day get there first shot, some day a little more, some a little less. So as of today, a total of at least 165 million have gotten at least on shot (50% of the entire population) and 65 million are fully vaccinated or 20% of the entire population. This is as of 4/4. So on my amended figures of some 270 million adult population, by 5/31 will need to have 202.5 million to be at 75% fully vaccinated.