Choose from an existing set of weights to make a target sum
MATL, 29 28 bytes
4t:qEZ^!&quot;[l2.5AX]@Y*10+G=?@.

For inputs that have no solution this produces an empty output (without error).
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Explanation
4           % Push 4
t:q         % Duplicate 4 and transform into range [0 1 2 3]
E           % Multiply by 2: transform into [0 2 4 6]
Z^          % Cartesian power. Each row is a &quot;combination&quot; of the four numbers
!           % Transpose
&quot;           % For each column
  [l2.5AX]  %   Push [1 2.5 5 10]
  @         %   Push current column
  Y*        %   Matrix multiply. Gives sum of products
  10+       %   Add 10
  G=        %   Compare with input: are they equal?
  ?         %   If so
    @       %     Push current column, to be displayed
    .       %     Break loop
            %   Implicit end
            % Implicit end
            % Implicit display