In Florida, the last three digits of a female with birth month $\displaystyle m$ and birth date $\displaystyle b$ are represented by $\displaystyle 40(m-1)+b+500$. For both males and females, the fourth and fifth digits from the end give the year of birth. Determine the dates of birth of people the the numbers whose last five digits are $\displaystyle 42218$ and $\displaystyle 53953$.

So the year of births for the two people are $\displaystyle 1918$ and $\displaystyle 1953$. Now $\displaystyle 40(m-1)+b+500 = 218$ and $\displaystyle 40(m-1)+b+500 = 953$ assuming both people are female. Then just guess and check to get $\displaystyle m$ and $\displaystyle b$? What if both are male?

2. Originally Posted by Sampras
In Florida, the last three digits of a female with birth month $\displaystyle m$ and birth date $\displaystyle b$ are represented by $\displaystyle 40(m-1)+b+500$. For both males and females, the fourth and fifth digits from the end give the year of birth. Determine the dates of birth of people the the numbers whose last five digits are $\displaystyle 42218$ and $\displaystyle 53953$.

So the year of births for the two people are $\displaystyle 1918$ and $\displaystyle 1953$. Now $\displaystyle 40(m-1)+b+500 = 218$ and $\displaystyle 40(m-1)+b+500 = 953$ assuming both people are female. Then just guess and check to get $\displaystyle m$ and $\displaystyle b$? What if both are male?
I would interpret "the fourth and fifth digits from the end" of 42218 and 53953 as being 42 and 53 respectively so the years of birth are 1942 and 1953, not 1918 and 1953. I notice that you then use 218 and 953, dropping the first two digits was that "1918" a typo?

The smallest that m or b can be is 1 so the smallest possible value for 40(m-1)+ b+ 500 is 500. That "218" is impossible. Perhaps this was a male?

40(m-1)+ b+ 500= 40m- 40+ b+ 500= 953 or 40m+ b= 493. Again, the largest that m can be is 12 and 40(12)= 480 so it is possible that m= 12, b= 13. If we were to try m= 11, 40(11)= 440 and 493- 440= 53. The only possible answer is m= 12, d= 13. The birthday is Dec. 13, 1953.

3. Originally Posted by HallsofIvy
I would interpret "the fourth and fifth digits from the end" of 42218 and 53953 as being 42 and 53 respectively so the years of birth are 1942 and 1953, not 1918 and 1953. I notice that you then use 218 and 953, dropping the first two digits was that "1918" a typo?

The smallest that m or b can be is 1 so the smallest possible value for 40(m-1)+ b+ 500 is 500. That "218" is impossible. Perhaps this was a male?

40(m-1)+ b+ 500= 40m- 40+ b+ 500= 953 or 40m+ b= 493. Again, the largest that m can be is 12 and 40(12)= 480 so it is possible that m= 12, b= 13. If we were to try m= 11, 40(11)= 440 and 493- 440= 53. The only possible answer is m= 12, d= 13. The birthday is Dec. 13, 1953.
isn't the smallest possible value $\displaystyle 501$?