–37of the people who live in an apartment building are men. 58of the remaining people are women. The rest are children. A total of 220 men and women live in the building. How many people live in the apartment building altogether?
37 + 58 = 95 ≠ 220
Let's break down the problem step by step:
Step 1: Calculate the number of men living in the apartment building.
If 37% of the people who live in the apartment building are men, then the remaining 63% are women and children.
Let's assume the total number of people living in the apartment building is x.
Therefore, the number of men in the apartment building is 0.37x.
Step 2: Calculate the number of women living in the apartment building.
If 58% of the remaining people are women, then the remaining 42% are children.
The number of women in the apartment building is 0.58 * 0.63x (58% of 63% of x), since we already accounted for the men.
Step 3: Calculate the total number of men and women living in the apartment building.
According to the problem, the total number of men and women living in the apartment building is 220.
So, 0.37x + 0.58 * 0.63x = 220.
Step 4: Solve for x.
Simplifying the equation, we have:
0.37x + 0.3634x = 220
0.7334x = 220
x = 220 / 0.7334
x ≈ 299.8
Step 5: Determine the number of people living in the apartment building altogether.
Since x represents the total number of people living in the apartment building, we round x to the nearest whole number.
The total number of people living in the apartment building is approximately 300.
Let's break down the information provided to find the solution step by step.
We know that initially, 37% of the people living in the apartment building are men. This means that if we consider the total population to be 100%, 37% of them are men.
So, let's assume that the total number of people living in the apartment building is "x". Therefore, the number of men in the building would be 0.37x.
According to the given information, 58% of the remaining people are women. Since we now subtracted the men from the total population, we have "x - 0.37x" people left. Therefore, 58% of this remaining population would be women.
Expressing this in equation form:
0.58(x - 0.37x) = 220
Now, let's solve the equation to find the value of "x."
0.58(0.63x) = 220
0.3654x = 220
x = 602.15
So, the total number of people living in the apartment building is approximately 602.
Therefore, there are 602 people living in the apartment building altogether.