I am thinking of two numbers. The smaller number is 25% of the bigger number. The sum of the numbers is 250. What is the difference hetween the two numbers

Answer 1

s = smaller number

b = bigger number

25% = 25 / 100 = 25 • 1 / 25 • 4 = 1 / 4

The smaller number is 25% of the bigger means:

s = b / 4

The sum of the numbers is 250.

s + b = 250

b / 4 + b = 250

Multiply both sides by 4

b + 4 b = 1000

5 b = 1000

b = 1000 / 5 = 200

s = b / 4 = 200 / 4 = 50

b - s = 200 - 50 = 150

Answer 2

Or without counting smaller and bigger numbers.

sum = bigger number + smaller number =

25% of the bigger number + 100% of the bigger number

sum = 125% of the bigger number

125% = 125 / 100 = 1.25

sum =1.25 of the bigger number

difference = bigger number - smaller number =

100% of the bigger number - 25% of the bigger number =

75% of the bigger number

75% = 75 / 100 = 0.75

difference= 0.75 of the bigger number

difference / sum =

0.75 of the bigger number / 1.25 of the bigger number

difference / sum = 0.75 / 1.25

difference / sum = 0.6

difference = 0.6 • sum

sum = 250 so:

difference = 0.6 • 250 = 150