Question 1005371: The sum of the digits of a two-digit number is 7. When the digits are exchanged, the number increased by 27. Find the number. Answer by ikleyn(52879) (Show Source):
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The sum of the digits of a two-digit number is 7. When the digits are exchanged, the number increased by 27. Find the number.
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Let a and b are the digits of your number n, so that n = 10a + b.
The number after interchanging digits is 10b + a.
Then you have the system of two equations for the unknowns a and b:
.
Now, simplify it:
.
Simplify it one more time:
.
Solve it.
The solution is b=5, a=2.
Hence, the number is 10a + b = 10*2+7 = 25.
Answer. 25.
See the lesson Word problems on interchanging digits of numbers for more problems like this one.
