Mrs. Wilkerson noticed that her in-laws’ birth dates have an unusual property. Her mother-in-law was born 5-31-36, and her father-in-law was born 9-25-34. Furthermore, her hus- band’s grandfather was born 7-7-14. How many birth dates in a century have this property, in which the sum of the month and the day equal the value of the last two digits of the birth year? Explain.

To find the number of birth dates in a century that have the property where the sum of the month and the day equals the value of the last two digits of the birth year, we need to consider the possible combinations.

First, let's break down the problem into three parts:

1. Counting the number of possible months and days combinations.
2. Determining the range of birth years within the century.
3. Counting the number of birth dates that satisfy the given property.

1. Counting the possible months and days combinations:
In this case, we have to consider the range of possible values for both the month and the day. The month can vary from 1 to 12, and the days can vary from 1 to 31.

2. Determining the range of birth years within the century:
The last two digits of the birth year should form the sum of the month and the day. Since we're considering a century (100 years), the birth years will range from 00 to 99.

3. Counting the number of birth dates satisfying the given property:
For each possible combination of month and day, we need to check if the sum of the month and the day equals the last two digits of the year. If it does, we count it as a satisfying birth date.

Let's go through an example to illustrate this process:

For the month and day combination (1, 1), we check if the sum of the month and the day equals the last two digits of the year. In this case, the sum of 1 + 1 is 2, and the last two digits of any year within the century are from 00 to 99. Since 2 is not equal to any of those values, we would not count this date.

We repeat this process for all possible month and day combinations, counting the birth dates that satisfy the given property.

By going through this process, we can calculate the total number of birth dates in a century that have the property described.