Question

Takashi's family is a family of five of his parents, older brother, Takashi and younger brother. Currently, Takashi is half the age of his brother and his brother is half his age. The total age of the whole family is 117 years old. After three years, the total age of the parents will be twice the total age of the brothers, including Takashi.

At this time, how many years from now will it be that 1.5 times the age of my brother equals the sum of the age of Takashi and my brother? _____ years later

let takashi's old brother = k so takashi =k/2 and takashi younger brother= k/4 so (k+3) + (k+3/2)+ (k+3/4) + 2* (k+3) + (k+3/2)+ (k+3/4)= 117+3 is this right?

Answer 1

Takashi's Family is of 5 members (parents,,older brother,,takashi,,younger brother)

let us take age of older brother = k

then age of takashi = k/2

and age of younger brother = k/4

given the total age of all family members is 117

After 3 years....

age of parents = twice of brothers age

age of brothers after 3 years ..

Older brother = k+3

takashi age = k/2 + 3

younger brother = k/4 +3

sum of all brothers = k+ k/2+k/4 +9 = 7k/4 +9 (let us take it as Y)

then age of parents = 2Y

sum of all ages = Y+ 2Y = 117 +3

=> Y = 40

=> k = 124/7 = 17.7

How many years from now it will be the 1.5 times of brother age is equals the sum of age of takashi and his brother..

After x years...

age of older brother = k+x = 17.7 + x

age of takashi = k/2 + x = 8.85 + x

age of younger brother = k/4 + x = 4.425 + x

as per condition... 1.5(17.7 +x ) = (8.85 + x)+ (4.425 + x)

   => 1.5 *17.7 + 1.5x = 13.275 + 2x

=> 26.55 - 13.275 = 0.5x

=> 0.5x = 13.275

=> x = 26.55

After 26.55 years,, the 1.5 times of brother age is equals the sum of age of takashi and his brother..