Question

At a party, ⅓ of the people are children. There are ⅗ as many men as women, and 5 more women than children. If the total number of people is x, form an equation in x and solve it.​

Answer 1

x= 60

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

`(10)/(15) x + (3)/(15) x + 8 = x`

`(13)/(15) x + 8 = x`

`x - (13)/(15) x = 8`

`(2)/(15) x = 8`

`x = 8 / (2)/(15)`

`x = 8 * (15)/(2)`

x= 4(15)

x= 60