The sum of the two 5 digit numbers ABC10 + ABC12 is 123422. What is A + B + C?

Accepted Solution

Answer:14Step-by-step explanation:We are given with two [tex]5\ digit[/tex] numbers whose first [tex]3 \ digits[/tex] are same.It is given that their sum is [tex]123422[/tex]adding the last two corresponding digits gives,[tex]0+2=2\\1+1=2[/tex]Now adding the rest,[tex]C+C \ should\ be\ 14[/tex] to get [tex]4[/tex][tex]1 \ carries\\B+B[/tex] should not give anything to carry as that will make A in decimal to satisfy the addition.Therefore,[tex]B+B \ has \ to \ be 1+1=2,+ 1 \ carry=3[/tex]Thus [tex]B= 1[/tex]And finally,[tex]A+A=12\\A=6[/tex]Thus [tex]A=6, B=1 \ and \ C=7[/tex]Now simplifying [tex]A+B+C\\=6+1+7\\=14[/tex]Thus [tex]14[/tex] is the answer.