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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.​

Sagot :

Leora03

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

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