I'm not quite sure where you're going with k vs k+1. we know that s + d = 209 (1) and we know that 6.5s + 2d = 836.5 (2) we can rewrite (1) as d = 209 -

I'm not quite sure where you're going with k vs k+1. we know that s + d = 209 (1) and we know that 6.5s + 2d = 836.5 (2) we can rewrite (1) as d = 209 - s (3) substituting (3) into (2) we get 6.5s + 2(209 - s) = 836.5 (4) solving (4) for s yields s = 93 (5) alternatively, you can solve the system of linear equations [ 1 1 ] [ s ] = [ 209 ] [ 6.5 2 ] [ d ] = [ 836.5 ] (1) [ s ] = [ -4/9 2/9 ] [ 209 ] [ d ] = [ 13/9 -2/9 ] [ 836.5 ] (2) [ s ] = [ 93 ] [ d ] = [ 116 ] (3)