SOLUTION: In a group of men, women, boys, and girls, there were 10 more men than boys and 5 more women than girls. If there are twice as many boys as girls and 105 people in all, how many ar

M = B+10

W = G+5

B = 2G

M+W+B+G = 105

(1)   M = B+10
(2)   W = G+5
(3)   B = 2G
(4)   M+W+B+G = 105

Using (3) substitute 2G for B in (1) and (4)

(5)   M = 2G+10
      M+W+2G+G = 105
(6)   M+W+3G = 105

So now our system is

(5)   M = 2G+10
(2)   W = G+5
(6)   M+W+3G = 105

Using (2) substitute G+5 for W in (6)

(6)   M+W+3G = 105
      M+G+5+3G = 105
(7)   M+4G = 100

Using (5), substitute 2G+10 for M in (7):

(7)   M+4G = 100
      2G+10+4G = 100
      6G = 90
(8)    G = 15

Using (8), substitute 15 for G in (7)

(7)   M+4G = 100
      M+4(15) = 100
      M+60 = 100
(9)      M = 40

That's the answer.  But to check we need W and B

Using (8), substitute 15 for G in (2)

(2)   W = G+5
      W = 15+5
      W = 20

Using (8), substitute 15 for G in (3)

(3)   B = 2G
      B = 2(15)
      B = 30

Answer: 40 men, 20 women, 30 boys, and 15 girls.

Checking:

That checks, because 40 is 10 more than 30

That checks, because 20 is 5 more than 15

That checks, because 30 is twice as many as 15

That checks because 40+20+30+15 = 105

Edwin