Respuesta :
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.
[tex]\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[/tex]
Hence, the number is 150.
(b)
Let 'b' be the number such that the quarter of his half is 48 i.e.
[tex]\dfrac{1}{4}(\dfrac{1}{2}b)=48\\\\\dfrac{1}{8}b=48\\\\b=48\times8\\\\b=384[/tex]
Hence the number is 384.
(c)
Let 'c' be the number such that the third quarter or, increased by 17 is 80.
[tex]\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[/tex]
Hence, the number is 84.
(d)
Let 'd' be the number such that its triplet, reduced by 28 is 755
[tex]3d-28=755\\\\3d=755+28=783\\\\d=\dfrac{783}{3}\\\\d=261[/tex]
Hence the number is 261.
(e
Let 'e' be the number such that double his third, increased by 80 is 400.
[tex]\\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[/tex]
Hence, the value of the number is 480.
