SOLUTION: please help me with this problem!!!" a bank teller accidentally reversed the digits in the amount of a check and overpaid a customer by $36. if the sum of the digits in the two-dig

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Question 246936: please help me with this problem!!!" a bank teller accidentally reversed the digits in the amount of a check and overpaid a customer by $36. if the sum of the digits in the two-digit amount was 10, what was the actual amount of the check?"
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
a bank teller accidentally reversed the digits in the amount of a check and overpaid a customer by $36. if the sum of the digits in the two-digit amount was 10, what was the actual amount of the check?"
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Let the original number be 10t+u where t is the tens digit and u is the units digit.
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The reversed number is 10u+t
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Equations:
t + u = 10
10u+t - (10t+u) = 36
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Rearrange:
t + u = 10
9u -9t = 36
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Simplify:
t + u = 10
-t+ u = 4
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Add and solve for "u":
2u = 14
u = 7
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Since t+u = 10, t = 3
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The original bill was $37
The overpayment bill was $73
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Cheers,
Stan H.

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Let the tens digit be represented by . Let the ones digit be represented by

The original amount of the check would then be represented by . The amount with the digits reversed would be . We know that one amount is 36 less than the other, so:

Which is to say:

Which is to say:

But we also know that the sum of the digits is 10, so:

Add this equation to the final form of the first equation:

So

And

Hence, the customer presented a check for $37 and received $73.

John