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Method to solve an equation

Mathematics Asked by Khosrotash on February 10, 2021

The question is: put one of $1,2,3,4,5,6,7,8,9$ in one position below, to obtain $100$
$$largeoverline{squaresquare}+overline{squaresquare}+overline{squaresquare}=100$$his mean fint
This mean to find three,two digit number with sum of 100.
I can find by guess and exam some of the possible answer like below
$$45+37+18=100\
46+35+19=100\65+23+12=100
$$
But I am looking for a $largetext {method}$ to solve the equation.
AS a second question, how to find all the possibilities? (when do not repeat any number)
Thanks in advance for any help.

One Answer

We need to solve

$$(10a+b)+(10c+d)+(10e+f)=100 implies 10(a+c+e)+b+d+f=100$$

and we have two cases

  • $b+d+f=10 implies a+c+e=9$
  • $b+d+f=20 implies a+c+e=8$

Answered by user on February 10, 2021

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