Question

The difference between two numbers is 25. The smaller number is 1/6th of the larger number. What is the value of the smaller number?

Answer 1

Let x = smaller number and y = bigger number.
y - x = 25 (positive difference given, so must be smaller subtracted from larger)
x = (1/6)y

Substituting (1/6)y in for x,

y - (1/6)y = 25
(5/6)y = 25
Times 6/5,
y = 150/5 = 30

x = (1/6)y = (1/6)*30 = 5

x is the smaller number, so the answer is 5.

Answer 2

Assuming X = larger number and Y smaller number then y=1/6x. So X-Y=25. Substituting 1/6X for Y then X-(1/6X) = 25. Remember 1X = 6/6X thus, (6/6X)-(1/6X)=25 then 5/6X=25 then 5X=(6*25)=150. X=30 thus Y is 5 (1/6 of 30).