In a town, 2/3 of the adult men are
married to 3/5 of the adult women.
The number of married men and
women are equal, and the adult
population is over 100. What is the
smallest possible number of adult
residents in the town?
To find the smallest possible number of adult residents in the town, we need to determine the lowest common multiple (LCM) of the fractions 2/3 and 3/5.
Step 1: Convert the fractions to have a common denominator.
The denominators 3 and 5 have a common multiple of 15, so we can convert the fractions accordingly:
- 2/3 becomes 10/15
- 3/5 becomes 9/15
Step 2: Find the LCM of the fractions.
The LCM of 10/15 and 9/15 is the same as the LCM of 10 and 9, which is 90.
Step 3: Determine the total number of adult residents.
Since the number of married men and women are equal, and the total adult population is over 100, the smallest possible number of adult residents in the town is 90+90= <<90+90=180>>180.
Therefore, the smallest possible number of adult residents in the town is 180.
To find the smallest possible number of adult residents in the town, we need to consider the fractions given in the problem.
Let's assume there are 'x' adult men and 'y' adult women in the town. According to the problem, 2/3 of the adult men are married, so the number of married men would be (2/3)x. Similarly, 3/5 of the adult women are married, so the number of married women would be (3/5)y.
The problem states that the number of married men and women is equal. Therefore, we can set up the following equation:
(2/3)x = (3/5)y
To simplify this equation, you can multiply both sides by the least common multiple (LCM) of the denominators, which in this case is 15:
15 * (2/3)x = 15 * (3/5)y
10x = 9y
From this equation, we can see that the number of adult men (x) and adult women (y) must be in the ratio of 10:9 in order for the number of married men and women to be equal.
Now, let's find the smallest possible values for 'x' and 'y' that satisfy this ratio and also ensure the total adult population is over 100.
To find the smallest values, we can start by setting 'x' to the smallest multiple of 10 that is greater than 100, which is 110. Then we can set 'y' to the smallest multiple of 9 that allows us to keep the ratio, which is 99.
So, the smallest possible number of adult residents in the town is x + y, which is 110 + 99 = 209. Therefore, the smallest possible number of adult residents in the town is 209.