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
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
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