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

Answer:

(a) 150

(b) 384

(c)  84

(d) 261

(e ) 480

Step-by-step explanation:

(a)

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

$\dfrac{1}{2}\times(\dfrac{1}{3}a)=25\\\\\dfrca{1}{2\times3}a=25\\\\\dfrac{1}{6}\times a=25\\\\a=25\times6\\\\a=150$    

Hence, the number is 150.

(b)

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

$\dfrac{1}{4}(\dfrac{1}{2}b)=48\\\\\dfrac{1}{8}b=48\\\\b=48\times8\\\\b=384$

Hence the number is 384.

(c)

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

$\dfrac{3}{4}c+17=80\\\\\dfrac{3}{4}c=80-17\\\\\dfrac{3}{4}c=63\\\\c=\dfrac{63\times4}{3}\\\\c=\dfrac{252}{3}\\\\c=84$

Hence, the number is 84.

(d)

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

$3d-28=755\\\\3d=755+28=783\\\\d=\dfrac{783}{3}\\\\d=261$

Hence the number is 261.

(e  

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

$\\2\dfrac{1}{3}e+80=400\\\\\dfrac{2}{3}e=400-80=320\\\\e=\dfrac{320\times 3}{2}\\\\e=\dfrac{960}{2}\\\\e=480$

Hence, the value of the number is 480.