5 ms·
I'm more perplexed by how to solve it, since any odd number of salads is a solution. I.e. for every k, 836.5 - 6.5 * (2 * k + 1) is an even number
by anon4 11y ago
I'm more perplexed by how to solve it, since any odd number of salads is a solution. I.e. for every k, 836.5 - 6.5 * (2 * k + 1) is an even number
- dastbe 11y agoI'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)
- castratikron 11y agoThat's how I did it. rref() on a TI83 is extremely useful.
- rtkwe 11y agoIt's a really standard form of 2 formula substitution, you're missing the fact that there was 209 drinks and salads sold combined which constrains the solution to a single answer. From the setup you get 2 equations where x is the number of salads and y is the number of drinks: > [1] 6.5x + 2 y = 836.5 and > [2] x + y = 209 Solve [2] for y and substitute into [1]: > 6.5*x + 2(209 - x) = 836.5 You can also do this with linear algebra but this is the way I would have known as a normal high schooler taking the SAT.