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6) The sum of the digits of a certain two-digit number is 8. Reversing its digits decreases the
number by 36. What is the number?

Sagot :

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Answer:

The number is 62

Step-by-step explanation:

Alright, let's say the first digit of the number is x and the second digit is y, making the number xy, then we are told that:

x+y = 8

As the sum of the two digits is equal to 8.

On top of this, we are also told that reversing the digits (xy becomes yx) decreases the original number (xy) by 36. Writing this into an equation:

yx = xy - 36

From the first equation, we find the following possibilities for number combinations:

[0,8] , [1,7] , [2,6] , [3,5] , [4,4] , [5,3] , [6,2] , [7,1] , [8,0]

Then, from the second equation we know that xy needs to be bigger than yx, since it decreases if you switch the numbers. This leaves out the first 5 possible combinations. Checking the others we find that:

[5,3] : 35 ≠ 53 - 36

[6,2] : 26 = 62 - 36 ←

[7,1] : 17 ≠ 71 - 36

[8,0] : 08 ≠ 80 - 36

There you go, the number has been found.

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