A number n is 25% of some number a and 35% of a number b ?is a>b?a<b? or is it impossible to determine the relationship

Question

perseverance with problems

 

Answer 1

Percents (%) may be written like 25% or decimal (like 0.25) or fractions (for example, 25/100).
 
The problem says that:
    n=(25/200)a
    n=(30/100)b
 
We may set the expressions for n to be equal to each other
 
   (25/100)a = (35/100)b
      a = (7/5)b                    [multiply both sides by 100/25]
 
Now,
  If a and are both positive, a>b
  If a and b are both zero, a=b (of course)
  If a and b are both negative, a<b

Note: a and b must have the same sign.

Answer 2

n = 0.25 a

n = 0.35 b

 

0.25a = 0.35b

25a = 35b

a = 1.4b

 

a > b