Tahrell has nutrition classes every 5 days and respiratory therapy classes every 9 day. If he had nutrition and respiratory therapy classes on October 19, on which date w he have both classes again? Assume the year is not a leap year.

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1. The nutrition classes are every $$5$$ days and the respiratory therapy classes every $$9$$ days. The classes will occur on the same day again after a number of days equal to the least common multiple of $$5$$ and $$9$$.

2. Compute the least common multiple:
   $$
   \text{LCM}(5, 9) = 45
   $$
   
3. Therefore, both classes will be held on the same day $$45$$ days after October $$19$$.

4. To find the new date, start by determining the number of days remaining in October:
   $$
   31 - 19 = 12 \text{ days}
   $$
   
5. Out of the $$45$$ days, $$12$$ days take you to October $$31$$. The remaining days are:
   $$
   45 - 12 = 33 \text{ days}
   $$
   
6. November has $$30$$ days. Subtracting these:
   $$
   33 - 30 = 3 \text{ days}
   $$
   
7. After November comes December, and $$3$$ days into December is:
   $$
   \text{December }3
   $$

Thus, Tahrell will have both classes again on **December $$3$$**.
Tahrell will have both classes again on December 3.

Tahrell has nutrition classes every 5 days and respiratory therapy classes every 9 day. If he had nutrition and respiratory therapy classes on October 19, on which date w he have both classes again? Assume the year is not a leap year.

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