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The sum of a 2-digit number and the 2-digit number when the digits are reversed is 77. If the difference of the same two numbers is 45, what are the two 2-digit numbers?

 Apr 5, 2020
 #1
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Let  t  be the ten's digit of the original number and  u  be the unit's digit of the original number.

This means that the original number is  10·t + u.

 

Reversing the digits, the new number is  10·u + t

 

Adding these numbers together, we get a sum of 77:  (10t + u) + (10u + t)  =  77

Simplifying:                                                                                    11t + 11u  =  77

Dividiing each term by 11:                                                                     t + u  =  7

 

Subtracting these numbers, we get a difference of 45:  (10t + u) - (10u + t)  =  45

Simplifying:                                                                                         9t - 9u  =  45

Dividing each term by 9:                                                                         t - u  =  5

 

Combining these two equations:            t + u  =  7

                                                                t - u  =  5

Adding down the columns:                         2t  =  12

Divide by 2:                                                  t  =  6

 

Substituting back into the equation  t + u  =  7   --->   6 + u  =  7   --->   u  =  1

 

You'll need to write the two numbers ...

 Apr 6, 2020

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