Question

The quotient of two positive integers is 21. The difference between the larger
integer and this quotient is 21. What is the sum of the two integers?

Answer 1

Let's call the larger integer x and the smaller integer y.

We are given that the quotient of the two integers is 21, which means x/y = 21.

We are also given that the difference between the larger integer and this quotient is 21, which means x - (x/y) = 21.

Substituting x/y = 21 into the second equation, we get x - 21 = 21.

Solving for x, we find x = 42.

Substituting x = 42 into the first equation, we get 42/y = 21.

Solving for y, we find y = 2.

The sum of the two integers is x + y = 42 + 2 = 44. Answer: \boxed{44}.