Subject: Question
Name: GG
Who are you: Student

The sum of two numbers is 30 and the product of the same two numbers is 221. Find the two numbers.


Hi GG.

15 + 15 is 30, but 15 times 15 is 225, so one of the numbers is higher than 15 and one of the numbers is lower than fifteen. We'll try to find the lower number (because it is easier working with smaller numbers and as soon as we find one number it is quick to find the other number).

The product is 221. That's an odd number, so the two factors must both be odd. What goes into 221?

If 3 goes in, then you could add the digits and get a multiple of 3:
2+2+1=5. No, not a multiple of 3.

If 5 goes in, it ends in 5 or 0. No.

If 3 doesn't go into a number, then 9 won't go into it either (because3 goes into 9).

So there are only 3 numbers left to check: 7, 11 or 13.

Do any of these go into 221? If so, find out what number you'd add to it to get 30 and see if that matches 221 divided by the first number.

Hope this helps,
Stephen La Rocque.