When the digits of a two-digit number are reversed, its value increases by 27. What is the number if the sum of its digits is 9?
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When the digits of a two-digit number are reversed, its value increases by 27. What is the number if the sum of its digits is 9?
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Solution:
Let:
xy = two-digit number
x = ones digit
y = tens digit
x + y = 9
10y + x = 10x + y + 27
10(9 - x) + x = 10x + (9 - x) + 27
90 - 10x + x = 10x + 9 - x + 27
-10x + x - 10x + x = 9 + 27 - 90
-18x = -54
x = 3
y = 9 - 3 = 6
To check:
36
3 + 6 = 9
63 = 36 + 27
63 = 63
Answer: 36