The sum of the two digits of a two-digits number is 9. The new number obtained by interchanging the digits exceeds the given numbe

2 thoughts on “The sum of the two digits of a two-digits number is 9. The new number obtained by interchanging the digits exceeds the given numbe”

1. Answer:

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2. Let x and y = the two digits

   Let x + y = 9 (Given)

   Let 10x + y = the first two digit number

   Therefore 10y + x = the two digit number with the digits interchanged

   The second two digit number is 27 larger than the first

   One possible equation would be 10x + y +27 = 10y +x

   (we are adding 27 to the smaller two digit so that the equation is balanced)

   Solve x + y = 9 for y

   y = (9 – x) [subtract x from both sides]

   Substitute (9 – x) for y in our equation

   10x + (9 – x) + 27 = 10(9 – x) + x

   Distribute the 10 (remember to do both 10(9) and 10x)

   10x + (9 – x) + 27 = 90 – 10x + x

   Simplify each side of the equation

   9x + 36 = 90 – 9x

   Add 9x to both sides

   18x + 36 = 90 (don’t forget 9x – 9x = 0 and 90 + 0 = 90)

   Subtract 36 from both sides

   18x = 54

   Divide both sides by 18

   x = 3 (again don’t forget 18/18 = 1 and 1x = x)

   Substitute 3 for x in the equation x + y = 9

   3 + y = 9 and solve for y (subtract 3 from both sides)

   3 – 3 + y = 9 – 3

   0 + y = 6

   y = 6

   THE DIGITS ARE 3 AND 6

   CHECK 36 + 27 = 63

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