Simultaneous Linear Equations
2009-07-20 6:53 pm
among the 40 employees of a company,half of the female employees and one-third of the male employees are married.If 16 employees of a company are married find the respective number of male and female employees in the company.
回答 (2)
2009-07-20 7:00 pm
✔ 最佳答案
suppose x = no. of female, y = no. of male x+y =40
0.5 x + 1/3 y = 16
sub x= 40- y
0.5 (40-y) + 1/3 y =16
20-0.5y +1/3 y =16
20-1/6y = 16
4= 1/6y
so y = 24
x = 16
check ok: 16*0.5 + 1/3 * 24 = 16
the key is to rearrange the equation so you have just a number on one side and only one symbol on the other.
hope it helps
2009-07-20 7:19 pm
Let a and b be the no. of female employees and the no. of male employees respectively.
40= a + b ---- ( 1 )
16=(a/2) + (b/3) ---- ( 2 )
For (1),
a=40-b -----(3)
Put (3) into (2) ,
16= (40-b)/2 + b/3
96=(40-b)(3) + 2b
96=120-3b+2b
b=24 ----(4)
Put (4) into (1)
40= a + 24
a=16
so the ans. is : a=16, b=24
40= a + b ---- ( 1 )
16=(a/2) + (b/3) ---- ( 2 )
For (1),
a=40-b -----(3)
Put (3) into (2) ,
16= (40-b)/2 + b/3
96=(40-b)(3) + 2b
96=120-3b+2b
b=24 ----(4)
Put (4) into (1)
40= a + 24
a=16
so the ans. is : a=16, b=24
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