Problema Solution
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
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let
x = the tens digit of the number
y = the ones digit of the number
the number is 10x + y
the sum of the digits of a certain two-digit number is 7
x + y = 7
reversing its digits increases the number by 9
the reversed number is 10y + x
10y + x = 10x + y + 9
by solving the system of equations
x + y = 7
10y + x = 10x + y + 9
we find
x = 3
y = 4
click here to see the step by step solution of the system of equations
the number is 3*10 + 4 = 34.