Question

The sum of the digits of a 2-digit number is 11. If the digits are reversed, the number formed is 45 more than the original number. Find the original number

Answer 1

the original number is 38

Explanation:

Let the two-digit number be 10t+u where t is the tens digit and u the units digit.

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EQUATION:

t+u = 11

10u+t = 10t+u + 45

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Rearrange the equations:

t+u = 11

9t-9u = -45

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Simplify:

t+u = 11

t-u = -5

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Add the equations to solve for "t":

2t = 6

t = 3

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Substitute to solve for "u":

3+u = 11

u = 8