[ab] = 10 a + b
a+b = 7
[ba] = 10 b + a = 9 + 10a + b
two equations
a + b = 7
and
10 b + a = 9 + 10 a + b
9 b = 9 + 9 a
b = 1 + a
combine
a + b - b = 7 - 1 - a
2 a = 6
a = 3
then b = 4
so answer is
34
check
34 + 9 = 43 sure enough
The sum of the digits of a certain two-digit number is 7. Reversing its digits increases the number by 9.
What is the number?
TIA
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