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ArbitrLikvidat [17]
3 years ago
13

3/7 of the people living in the apartment building are men. 5/8 of the remaining are women. The rest are children. A total of 27

5 men and women live in the building. How many people live the the building altogether?
Mathematics
1 answer:
Vladimir [108]3 years ago
7 0
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!

hope this is right! have a great. day
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The statement is now presented as:

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In other words, this mathematical statement can be translated as:

<em>There is a point (h, k) in the set of real ordered pairs so that a circumference centered at (h,k) and with a radius r implies a equivalent circumference centered at (h+4,-k) and with a radius r. </em>

Step-by-step explanation:

Let C = (h,k) the coordinates of the center of the circle, which must be transformed into C'=(h', k') by operations of translation and reflection. From Analytical Geometry we understand that circles are represented by the following equation:

(x-h)^{2}+(y-k)^{2} = r^{2}

Where r is the radius of the circle, which remains unchanged in every operation.

Now we proceed to describe the series of operations:

1) <em>Center of the circle is translated 4 units to the right</em> (+x direction):

C''(x,y) = C(x, y) + U(x,y) (Eq. 1)

Where U(x,y) is the translation vector, dimensionless.

If we know that C(x, y) = (h,k) and U(x,y) = (4, 0), then:

C''(x,y) = (h,k)+(4,0)

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2) <em>Reflection over the x-axis</em>:

C'(x,y) = O(x,y) - [C''(x,y)-O(x,y)] (Eq. 2)

Where O(x,y) is the reflection point, dimensionless.

If we know that O(x,y) = (h+4,0) and C''(x,y) =(h+4,k), the new point is:

C'(x,y) = (h+4,0)-[(h+4,k)-(h+4,0)]

C'(x,y) = (h+4, 0)-(0,k)

C'(x,y) = (h+4, -k)

And thus, h' = h+4 and k' = -k. The statement is now presented as:

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<em />

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