Question

A magician asks a volunteer to think of two different positive integers without telling her what they are. She then asks him to calculate x, the sum of the larger number with the square of the smaller, and y, the difference between the numbers. The volunteer tells her that x = 9 and y = 3. Find the original numbers.

Answer 1

the original numbers are 5 and 2

Explanation:

fistly it says inorder to find x one has to add the larger number to the square of the smaller number. So in this case start off with smaller guesses of positive integers as it is simpler that way.

the first guesses that would end up giving you 9 as an answer is 5 and 2

• 5+(2×2)=9

So now that the integers chosen fit in when calculating x we have to check if it also checks out in calculating y.

For y the difference between the 2 integers have to give an answer of 3. after calculations it the numbers comply to the statement for y;

• 5-2=3

hence the answers are 5 and 2