Question

A positive number is 5 times another number. If 21 is added to both the numbers, then one of the new numbers becomes the other new number. What are the numbers?

Answer 1

let two numbers are y and 5y if we add 21 they will become y+21 and 5y+21
5y + 21 = 2*(y + 21)
5y + 21 = 2y + 42 Distributing on the right-hand side
3y + 21 = 42 Subtracting 2y from both sides
3y = 21 Subtracting 21 from both sides
y = 7 Dividing both sides by 7
Thus, y = 7 and x = 5y = 5*7 = 35, so the two numbers are 7 and 35.