3/7 of the people who live in an apartment building are men. 5/8 of 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?

Question

Illustrate an apartment building with windows acting as visual representation of its inhabitants. Depict 3/7ths of the building's windows with silhouettes of men, followed by 5/8ths filled with silhouettes of women. Leave some windows empty to signify children. The building should be sizable but not gigantic, hinting at the total of 220 men and women living there. Surroundings can include a common urban setting with a clear, sunny day. Ensure the image does not have any text.

3/7 of the people who live in an apartment building are men. 5/8 of 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?

Answer 1

people in building ---- x (men, women and children)

children --- y
men + women + children = x
(3/7)x + (5/8)(4/7)x + y = x
3x/7 + 5x/14 + y = x
times 14
6x + 5x + 14y = 14x
14y = 3x

y + 220 =x
sub into the other one
14y = 3(y+220)
11y = 660
y = 60
then 14(60) = 3x ---> x = 280

So we have 280 people in the building.

check: 3/7 of 280 are men = 120
leaving 160 women and children
5/8 of these ot 100 are women

so we have 120 men, 100 women and 60 children.

Answer 2

thanks, there was a similar problem instead of 220 men and women it was 275.. i just substituted

Answer 3

where is 4/7 from

Answer 4

Well, if 3/7 of the people in the apartment building are men, that means that 4/7 are not men. And if we know that 5/8 of those remaining people are women, that means 3/8 are not women. So now we have 4/7 * 3/8 = 12/56 of the people are children.

Now, let's do some math with this information. We know that a total of 220 men and women live in the building. So if we add the men, women, and children together, that would be:

220 + (220 * 12/56) = 220 + 47.14 (rounding to the nearest whole number) = 267

So, there are approximately 267 people living in the apartment building altogether.

Answer 5

To find the total number of people in the apartment building, we'll work step by step.

Let's use algebraic expressions to represent the steps:

Let's assume:
Total number of people in the apartment building = x

Step 1:
Given that 3/7 of the people who live in the apartment building are men, we can represent this as (3/7) * x = number of men.

Step 2:
Now, we know that 5/8 of the remaining people, which means (1 - 3/7), are women. So, we calculate this as (5/8) * (4/7) * x = number of women.

Step 3:
We add the number of men and women together and set it equal to the total number of men and women (220) to solve for x:
(3/7) * x + (5/8) * (4/7) * x = 220

Let's simplify and solve the equation:

(3/7) * x + (5/8) * (4/7) * x = 220
(3/7) * x + (5/2) * (1/7) * x = 220 (Simplified the fractions)
(3/7) * x + (5/14) * x = 220 (Multiplication)
(42/98) * x + (10/14) * x = 220 (Simplified the fractions)

Now, let's determine a common denominator for the fractions:
(42/98) * x + (10/14) * x = 220
(42/98) * x + (5/7) * x = 220 (Multiplied (10/14) by 2/2)

Now, we can add the fractions:
((42/98) + (5/7)) * x = 220

Now, let's calculate the sum of the fractions:
(42/98) + (5/7) = (294/686) + (490/686) = 784/686 = 112/98

So, the equation becomes:
(112/98) * x = 220

Now, we can solve for x by multiplying both sides by (98/112):
x = (220 * (98/112))

x ≈ 191.67

Therefore, there are approximately 192 people living in the apartment building altogether.