In a particular tour group, 30% of the tourists are men, and there are 20 more women than men. How many tourists altogether are there in the group? Explain your reasoning.
To find the total number of tourists in the group, we need to understand the relationship between the number of men and women.
Let's assume the total number of tourists in the group is "T."
Given that 30% of the tourists are men, we can say that 30% of T is the number of men. Mathematically, this can be written as 0.30T.
The problem also states that there are 20 more women than men. We can represent the number of women as the number of men plus 20. So, the number of women would be (0.30T + 20).
Now, we can calculate the total number of tourists by adding the number of men to the number of women:
Total number of tourists = number of men + number of women
Total number of tourists = 0.30T + (0.30T + 20)
To solve for T, we need to simplify the equation:
Total number of tourists = 0.30T + 0.30T + 20
Total number of tourists = 0.60T + 20
Since the given information mentions that the total number of tourists is "T," we can set up an equation to solve for T:
T = 0.60T + 20
To solve the equation, we can isolate the "T" term:
T - 0.60T = 20
0.40T = 20
Dividing both sides of the equation by 0.40, we find:
T = 20 / 0.40
T = 50
Therefore, there are 50 tourists altogether in the group.