Rob was looking at his collection of band concert programs, from all the band concerts that he has ever been in. There were less than 100
programs altogether. He started organizing the programs into piles. He
put all the programs into piles of 4, but found there were three left
over. So then he put them in piles of 5, and again found there were 3
left over. Next he tried putting them into piles of 7, and this time found
there were 6 left over. Finally he put them into piles of 3, and this time
there were 2 left over. So he gave up and stuck them back in the drawer
where he found them. How many programs does Rob have?

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answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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rauschg

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