How many people?
In a village, there are exactly:
10% more boys than girls
15%more women than men
20% more children than adults
If the population of the village is less than 6000, find the actual population of the village.
Note: the population cannot be decimal since we are dealing people.
The answer is 3311.
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1 solution
Let the number of boys be b, the number of girls be g, the number of men be m, and the number of women be w.
There are 10% more boys than girls i.e
b= (10/100)*g+ g.
b=0.1g+ g
b=1.1g
number of children (C) = boys + girls
C= 1.1g+ g
C= 2.1g.
There are 15% more women than men i.e
w=(15/100)*m +m
w= 0.15m+m
w=1.15m
number of adults(A) =men +women
A=1.15m+m
A=2.15m
There are 20% more children than adults i.e
C=(20/100)*A+A
C= 0.2A+A
C=1.2A
2.1g=1.2*2.15m
2.1g= 2.58m………………………………eq(1)
Total population of village is less than 6000
2.1g+2.58m< 6000 ……………………….eq2
From eq1 g=2.58m/2.1 sub into eq2
2.1*(2.58m/2.1)+2.58m<6000
2.58m+2.58m<6000
5.16m<6000
m<6000/5.16
m<1162.8
The number of people cant be decimal
m<1162
g=2.58m/2.1...................................eq3
numbers less than 1162 when multiplied by 2.58/2.1 give a whole number are (35,70,105,140,175,210,245,.., 1155)
therefore m can be 35,70,105,140,175,..., 1155
by substituting the value of m into eq3, g can be 43,86,129,172,215,..., 1419
b= 1.1g by substituting g, only one value of g gives a whole number (860)
b=1.1*860
b=946
w=1.15m by substituting m, only one value of m gives a whole number(700)
w= 1.15*700
w=805
Therefore the population of the village= 700+ 860+ 946+ 805
=3311