SOLUTION: When you reverse the digits in a certain two-digit number you decrease its value by 9. What is the number if the sum of its digits is 13?

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Question 989101: When you reverse the digits in a certain two-digit number you decrease its value by 9. What is the number if the sum of its digits is 13?

Found 2 solutions by zhagi17, josmiceli:
Answer by zhagi17(16) About Me  (Show Source):
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the units digit = +b+
Let the tens digit = +a+
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given:
(1) +a+%2B+b+=+13+
(2) +10a+%2B+b+=+10b+%2B+a+%2B+9+
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(2) +9a+-+9b+=+9+
(2) +a+-+b+=+1+
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Add (1) and (2)
(1) +a+%2B+b+=+13+
(2) +a+-+b+=+1+
-------------------
+2a+=+14+
+a+=+7+
and
(2) +a+-+b+=+1+
(2) +b+=+a+-+1+
(2) +b+=+7+-+1+
(2) +b+=+6+
-------------------
The number is 76
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check:
Reverse the digits: 67
+76+-+67+=+9+
and
+7+%2B+6+=+13+
OK