tag:blogger.com,1999:blog-15628310.post6920204810636397353..comments2022-07-26T20:48:08.865-04:00Comments on Question of the day: Check, PleaseAnonymoushttp://www.blogger.com/profile/18153935609499338685noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-15628310.post-14592999432625361702010-02-10T12:22:43.320-05:002010-02-10T12:22:43.320-05:00In case anyone cares to know, the way I found this...In case anyone cares to know, the way I found this one was sort of a brute force method. I got the equation that Mike mentioned, and solved for x:<br /><br />x = (97y - 50)/299<br /><br />Then I used a quick spreadsheet to find x for all possible values of y (00...99), and found that x=18, y=56 was the only one that came out to integer values, so that was my answer.<br /><br />Not sure if the spreadsheet is considered cheating though :)Andyhttps://www.blogger.com/profile/14117563810484999900noreply@blogger.comtag:blogger.com,1999:blog-15628310.post-38915905710307905792010-02-10T09:52:10.763-05:002010-02-10T09:52:10.763-05:00Let x be the number of dollars in the check, and y...Let x be the number of dollars in the check, and y be the number of cents.<br /><br />Then 100y + x − 50 = 3(100x + y).<br /><br />Therefore 97y − 299x = 50.<br /><br />Keep in mind that x and y have to be between 0 and 100<br /><br />It can be shown that all integer solutions of 97y − 299x = 50 are of the form y = 1850 + 299k, x = 600 + 97k, where k is any integer. (I'm not going to show this... too much writing!)<br /><br />In this case, because x and y must be between 0 and 99, we choose k = −6.<br /><br />This gives y = 56, x = 18.<br /><br />So the check was for $18.56.Anonymoushttps://www.blogger.com/profile/18153935609499338685noreply@blogger.comtag:blogger.com,1999:blog-15628310.post-84591557643702125962010-02-09T11:35:59.503-05:002010-02-09T11:35:59.503-05:00we ARE extremely rusty in our
algebraic skills. :...we ARE extremely rusty in our<br />algebraic skills. :-)<br /><br />we spent an inordinate (pun!)<br />amount of time juggling<br /> x's, y', a' & b's with nothing<br />to show for it except a proper humbling.<br /> {our guess is that it was overdue}<br /><br />we were able, however,<br />to confirm Andy's answer through other means.<br /><br />it appears that $18.56 is correct. kudos!<br /><br />and thanks for the twister<br /><br />..<br />.erobARE-eYED sUNhttps://www.blogger.com/profile/09274024134490490172noreply@blogger.comtag:blogger.com,1999:blog-15628310.post-54709498526631574962010-02-09T10:20:13.382-05:002010-02-09T10:20:13.382-05:00$18.56$18.56Andyhttps://www.blogger.com/profile/14117563810484999900noreply@blogger.com