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24% of the people at a shopping mall are men. The number of boys is 3/8 of the number of men. The number of women is 4 times the number of boys. The number of girls is 504 more than the number of men. How many males are there in the shopping mall?(please answer in a specific primary 5 way as my nephew is primary5)

MaiaMitchell  Aug 10, 2015

Best Answer 

 #1
avatar+20024 
+15

24% of the people at a shopping mall are men. The number of boys is 3/8 of the number of men. The number of women is 4 times the number of boys. The number of girls is 504 more than the number of men. How many males are there in the shopping mall?

x are the number of all people.

m = men,  b = boys, w = women, g = girls

 

$$\small{
\begin{array}{rcl}
m&=& 0,24x\\\\
b&=& \dfrac{3}{8}m \\
w &=& 4\cdot b = 4\cdot \dfrac{3}{8}m = \dfrac{3}{2}m\\
g &=& 504 + m\\\\
x &=& m+b+w+g\\\\
x &=& m + \dfrac{3}{8}m+\dfrac{3}{2}m+504 + m\\\\
x &=& 2m+ \dfrac{3}{8}m+\dfrac{3}{2}m+504 \\\\
x &=& \dfrac{16+3+12}{8}m+504\\\\
x &=& \dfrac{31}{8}m+504\\\\
x &=& \dfrac{31}{8}\cdot 0.24x+504\\\\
x &=& 31\cdot 0.03x+504\\\\
x &=& 0.93x+504\\\\
x- 0.93x &=&504\\\\
0.07x &=&504\\\\
x &=& \dfrac{504\cdot 100}{7}\\\\
x &=& 7200\\\\
m &=& 0.24x\\
m &=& 0.24\cdot 7200 \\
\mathbf{m} & \mathbf{=} & \mathbf{1728}
\end{array}
}$$

 

There are 1728 males in the shopping mall

Boys = 648

Woman = 2592

Girls = 2232

 

heureka  Aug 10, 2015
 #1
avatar+20024 
+15
Best Answer

24% of the people at a shopping mall are men. The number of boys is 3/8 of the number of men. The number of women is 4 times the number of boys. The number of girls is 504 more than the number of men. How many males are there in the shopping mall?

x are the number of all people.

m = men,  b = boys, w = women, g = girls

 

$$\small{
\begin{array}{rcl}
m&=& 0,24x\\\\
b&=& \dfrac{3}{8}m \\
w &=& 4\cdot b = 4\cdot \dfrac{3}{8}m = \dfrac{3}{2}m\\
g &=& 504 + m\\\\
x &=& m+b+w+g\\\\
x &=& m + \dfrac{3}{8}m+\dfrac{3}{2}m+504 + m\\\\
x &=& 2m+ \dfrac{3}{8}m+\dfrac{3}{2}m+504 \\\\
x &=& \dfrac{16+3+12}{8}m+504\\\\
x &=& \dfrac{31}{8}m+504\\\\
x &=& \dfrac{31}{8}\cdot 0.24x+504\\\\
x &=& 31\cdot 0.03x+504\\\\
x &=& 0.93x+504\\\\
x- 0.93x &=&504\\\\
0.07x &=&504\\\\
x &=& \dfrac{504\cdot 100}{7}\\\\
x &=& 7200\\\\
m &=& 0.24x\\
m &=& 0.24\cdot 7200 \\
\mathbf{m} & \mathbf{=} & \mathbf{1728}
\end{array}
}$$

 

There are 1728 males in the shopping mall

Boys = 648

Woman = 2592

Girls = 2232

 

heureka  Aug 10, 2015
 #2
avatar+89865 
+10

Let T be the total number of people......

 

The, the men = .24T ....  The number of boys =(3/8)*.24T = .09T ..... The number of women = .36T   and The number of girls =  (1 - .24 - .09 - .36)T  = .31T

 

And we know that

 

.24T + 504  = .31T      subtract . 24T from both sides

 

.07T  = 504        divide both sides by .07

 

T =504/.07 = 7200 = T = the total number of people

 

And the number of males = (.24 + .09)(7200)  = .33(7200)  = 2376

 

And the number of females is (.31 + .36)T = (.67)(7200)  = 4824

 

 

  

CPhill  Aug 11, 2015
 #3
avatar+93644 
0

There seems to be some disagreement here.    

Melody  Aug 12, 2015
 #4
avatar+89865 
+5

Actually, Melody.....I think heureka meant to say that there are 1728 men in the mall.....if you add this to the 648 boys, you have my answer of 2376 males

 

 

 

  

CPhill  Aug 12, 2015
 #5
avatar+93644 
0

Thanks for clearing that up Chris :))

Melody  Aug 12, 2015

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