Question

A boy is twice as tall as his little sister and 30cm shorter than his father. Their combined height is 3.8 meters. Find (in cm) the height of each person.

Answer 1

Height of boy = 140 cm

Height of sister = 70 cm

Height of father = 170 cm

Explanation:

Given that:

Combined height = 3.8 meters = 3.8*100 = 380 cm

Let,

b be the height of boy

s be the height of sister

f be the height of father

According to given statement;

b + s + f = 380 Eqn 1

b = 2s Eqn 2

b = f - 30 Eqn 3

Putting b=2s in Eqn 3

2s = f - 30

`s=(f-30)/(2)`

Putting these values in Eqn 1

`f-30+(f-30)/(2)+f=380\\(2f-60+f-30+2f)/(2) = 380 \\\\5f - 90 = 760 \\5f = 760+90 \\5f = 850`

Dividing both sides by 5

`(5f)/(5)=(850)/(5)\\f=170`

Putting f=170 in Eqn 3

b = 170 - 30

b = 140

Putting f=170 in Eqn 2

140 = 2s

s = 70

Hence,

Height of boy = 140 cm

Height of sister = 70 cm

Height of father = 170 cm