Question 1049560
The error comes about by being {{{inconsistent}}} in how you account for where  the ${{{5}}} in change went after the purchase of the shoes,

first you used the ${{{5}}} in change to give to your friend ${{{3}}} and from remaining ${{{2}}} you erroneously subtract ${{{1}}} from what you owe each of your mom and sister (${{{25}}} - ${{{1}}} = ${{{24}}}) (you're counting backwards!) and then you  {{{added}}} to that total debt balance of  ${{{48}}} (${{{24}}} you owe mom + ${{{24}}} you owe sister) and the ${{3}}} which you gave to your friend  then arrive at the false sum of ${{{51}}}, when you should have correctly and {{{consistently}}} added the ${{{5}}} change back onto the ${{{45}}}-cost of the shoes so that the correct total balance of ${{{50}}} would then be realized and accounted for as follows:


BEFORE THE PURCHASE OF THE SHOES
Amount borrowed from mom -- ${{{25}}}
Amount borrowed from sister   --  ${{{25}}}
Total borrowed                          --  ${{{50}}}
 
-------------------------------------------------------------------------
 
AFTER THE PURCHASE OF THE SHOES
Cost of shoes                              --     $ {{{45}}}
plus $ {{{5}}} change:
three dollars to friend           --     ${{{3}}}
One dollar to mom                  --     ${{{1}}}
One dollar to sister                    --     ${{{1}}}

Total                                                  ${{{50}}}


or simply, you add  ${{{cost-of-shoes+1(mom)+1(sister)+3(friend)=45+1+1+3=50}}}