SOLUTION: Solve the question using matrices: The sum of the digits of a certain two digit # is 12. Reversing its digits decreases the # by 18. What is the number?

Question 1171469: Solve the question using matrices:
The sum of the digits of a certain two digit # is 12. Reversing its digits decreases the # by 18. What is the number?
Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!



N=10a+b



Given:

a + b = 12   (1)



and "digits reversed decreases # by 18" tell us:

10b + a = (10a+b)-18



which simplifies to

 -9a + 9b = -18   (2)



multiply (1) by 9 and add to (2) to get:

 9a + 9b = 108

 -9a + 9b = -18

-----------------

      18b = 90  -->  b=5 --> a=7  -->  



Check:

 7+ 5 = 12  (ok on sum of digits)

 75 - 18 = 57  (ok on digits reversed)

 

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