Assume, m=men, w=women, and c=child, and m >
0, w >
0, and c >
0
4m + 2w + [( ¼) c] = 40 ………………………….(1)
m + w + c = 40 ……………………………………..(2)
c value should be a multiple of 4,
and
The value ( ¼) c should be an EVEN number and at least less than or equal 34
(since there should be at least one man and one women),
To satisfy both above observations about “c” , We can assume c = 8x, where x can be 1, 2, 3, or 4.
So x
<= 4 …………………………………..(3)
Substitute in above equations:
4m + 2w + 2x = 40 Or
2m + w + x = 20 ……………………………………….(4)
m + w + 8x = 40 ……………………………………….(5)
sub (4) from (5) ---------------
7x – 20 = m ………………………………………(6)
Or m + 20 = 7x
But from the fact that, m >
0 and x
<= 4, that’s mean 7x
<= 28
And from (6)
M + 20
< 28 then m
< 8, and also m
<0 ,
Then
0
< m
< 8 , sub the value of m from (6), 7x – 20 = m,
0
< 7x – 20
< 8 ------- 20
< 7x
< 28 ------- (20/7)
< x
< 4 ------------ 2 6/7
< x
< 4 .
Then x = 3, c = 8x = 24 , m = 7x – 20 =21 -20 =1, and w =15.
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