Question

Марина записала дату своего рождения (число,месяц и год).Потом она умножила число на номер месяца и получила 372.Когда у неё день рождение?найдите все варианты и докажите,что нет других

Answer 1

372:12=31
значит Марина родилась 31 декабря.
372:2=186
372:3=124
372:4=93
372:5=74,4
372:6=62
372:7=53,1
372:8=46,5
372:9=41,3
372:10=37,2
372:11=33,8
372:12=31
Подходит один вариант.

Answer 2

Problem Analysis

Marina multiplied the day of her birth by the month number and obtained a result of 372. We need to find all possible dates of her birthday and prove that there are no other options.

Solution

To find all possible dates of Marina's birthday, we need to consider the factors of 372 and check if they correspond to valid dates.

The factors of 372 are: - 1 and 372 - 2 and 186 - 3 and 124 - 4 and 93 - 6 and 62 - 12 and 31 - 13 and 28 - 31 and 12 - 62 and 6 - 93 and 4 - 124 and 3 - 186 and 2 - 372 and 1

Now, let's check if any of these factor pairs correspond to valid dates.

1. The factor pair (1, 372) does not correspond to a valid date because the month cannot be 372. 2. The factor pair (2, 186) does not correspond to a valid date because the month cannot be 186. 3. The factor pair (3, 124) does not correspond to a valid date because the month cannot be 124. 4. The factor pair (4, 93) does not correspond to a valid date because the month cannot be 93. 5. The factor pair (6, 62) does not correspond to a valid date because the month cannot be 62. 6. The factor pair (12, 31) corresponds to a valid date because the month can be 12 and the day can be 31. However, this is not a possible date because December only has 31 days, not 31 months. 7. The factor pair (13, 28) corresponds to a valid date because the month can be 13 and the day can be 28. However, this is not a possible date because there are only 12 months in a year. 8. The factor pair (31, 12) corresponds to a valid date because the month can be 31 and the day can be 12. However, this is not a possible date because there are only 12 months in a year. 9. The factor pair (62, 6) does not correspond to a valid date because the month cannot be 62. 10. The factor pair (93, 4) does not correspond to a valid date because the month cannot be 93. 11. The factor pair (124, 3) does not correspond to a valid date because the month cannot be 124. 12. The factor pair (186, 2) does not correspond to a valid date because the month cannot be 186. 13. The factor pair (372, 1) does not correspond to a valid date because the month cannot be 372.

Therefore, there are no valid dates that satisfy the condition of multiplying the day by the month to obtain 372. Marina's birthday cannot be determined based on the given information.

Conclusion: There are no possible dates for Marina's birthday that satisfy the condition of multiplying the day by the month to obtain 372.