Find four numbers so that same answer is obtained when: a. 4 is added to first b. 4 is subtracted from second...

Question

Find four numbers so that the same answer is obtained when:
(a) 4 is added to the first
(b) 4 is subtracted from the second
(c) the third is multiplied by 4
(d) the fourth is divided by 4.

Clue: they add up to 75.

Answer 1

let the numbers be abcd
a+b+c+d=75
a+4=x
b-4=x
4c=x
d/4=x
a+4=b-4 a=b-8
4c=b-4 c=b/4-1
d/4=b-4 d=4b-16
b-8+b+b/4-1+4b-16=75
6b+b/4=100
25b=400
b=16
a=16-8
a=8
c=16/4-1
c=3
d=4*16-16
d=48