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Find Number Pairs

Activities

The numbers 12 and 60 have a fascinating property: if we multiply them together, we get exactly 10 times more than if we add them up:

12 x 60 = 720, 12 + 60 = 72.

Try and find another pair like this. Maybe you can find several pairs with the same property.

Solution

The following are the four other pairs of such numbers: 11 and 110; 14 and 35; 15 and 30; 20 and 20.

In fact,

11 x 110 = 1,210; 11 + 110 = 21;

14 x 35 = 490; 14 + 35 = 49;

15 x 30 = 450; 15 + 30 = 45;

20 x 20 = 400; 20 + 20 = 40.

The problem has no other solutions. Searching for the solutions by trial and error is tiresome and knowledge of the ABC of algebra would make the process easier and enable us not only to find all the solutions, but also to make sure that the problem doesn't have more than five solutions.

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Source: Numeracy Counts !, Anita Rampal, R Ramanujam and L S Saraswati, N L R C, LBS National Academy of Administration, Mussoorie.

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