Three-fourths of a number is equal to 60% of another number and the difference between these two number is 20. What is the sum of these two numbers?

Question: Three-fourths of a number is equal to 60% of another number and the difference between these two number is 20. What is the sum of these two numbers?

Solution:
Let the numbers be x and x + 20

Then,
3x/4 = 60% of (x + 20)
⇒ 3x/4 = 60(x + 20)/100
⇒ 3x/4 = 3(x + 20)/5
⇒ x/4 = (x + 20)/5
⇒ 5x = 4x + 80
⇒ 5x - 4x = 80
⇒ x = 80

The sum of these two numbers = x + x + 20
= 2x + 20
= 2 × 80 + 20
= 160 + 20
= 180