Answer:
x= 60
Step-by-step explanation:
Total number of people= x
Let the number of children, men and women be c, m and w respectively.
c= ⅓x -----(1)
m= ⅗w -----(2)
w= c +5 -----(3)
Substitute (1) into (3):
w= ⅓x +5 ----(4)
Substitute (4) into (2):
m= ⅗(⅓x +5)
m= ⅕x +3 -----(5)
Since the total number of people is x,
c +m +w= x -----(6)
Substitute (1), (5) and (4) into (6):
⅓x +⅕x +3 +⅓x +5= x
⅔x +⅕x +8= x
[tex] \frac{10}{15} x + \frac{3}{15} x + 8 = x[/tex]
[tex] \frac{13}{15} x + 8 = x[/tex]
[tex]x - \frac{13}{15} x = 8[/tex]
[tex] \frac{2}{15} x = 8[/tex]
[tex]x = 8 \div \frac{2}{15} [/tex]
[tex]x = 8 \times \frac{15}{2} [/tex]
x= 4(15)
x= 60
