Question

Afla un numar,stiind ca: a)jumatatea treimii lui este 25; b)sfertul jumatatii lui este 48; c)treimea sfertului sau,marita cu 17 este 80; d)triplul jumatatii lui,micsorat cu 28 este 755; e)dublul treimii lui,marit cu 80 este 400.

Answer 1

(a) 150

(b) 384

(c) 84

(d) 261

(e ) 480

Explanation:

(a)

Let 'a' be a number such that the half of his third is 25; i.e.

`(1)/(2)*((1)/(3)a)=25\\\\\dfrca{1}{2*3}a=25\\\\(1)/(6)* a=25\\\\a=25*6\\\\a=150`

Hence, the number is 150.

(b)

Let 'b' be the number such that the quarter of his half is 48 i.e.

`(1)/(4)((1)/(2)b)=48\\\\(1)/(8)b=48\\\\b=48*8\\\\b=384`

Hence the number is 384.

(c)

Let 'c' be the number such that the third quarter or, increased by 17 is 80.

`(3)/(4)c+17=80\\\\(3)/(4)c=80-17\\\\(3)/(4)c=63\\\\c=(63*4)/(3)\\\\c=(252)/(3)\\\\c=84`

Hence, the number is 84.

(d)

Let 'd' be the number such that its triplet, reduced by 28 is 755

`3d-28=755\\\\3d=755+28=783\\\\d=(783)/(3)\\\\d=261`

Hence the number is 261.

(e

Let 'e' be the number such that double his third, increased by 80 is 400.

`\\2(1)/(3)e+80=400\\\\(2)/(3)e=400-80=320\\\\e=(320* 3)/(2)\\\\e=(960)/(2)\\\\e=480`

Hence, the value of the number is 480.