# 1) The tourist decided to pass 252 km. As he passed in day 3 km bigger, than is planned, spent for all way 2 days smaller. How many days did the tourist's campaign proceed? 2) It is required to pack into boxes of 378 identical objects so that in boxes was these objects equally. Esli to put in each box 9 objects more, than it is provided, it is required 1 box less. How many it is required boxes? 3) It is possible to place 640 identical books in a knizhny rack, equally on each of shelves. The shelf to place Esli for a kazhda 8 books more, than it is planned, 4 shelves will remain empty. How many shelves in this rack?

Vavila

53

1) The tourist had to go with v speed during t of days. = 252 It passed v*t on 3 km a day more and came 2 days faster. (v + 3) (t - 2) = v*t = 252 v*t + 3t - 2v - 6 = v*t 3t - 2v - 6 = 0 v = (3t - 6)/2 v*t = t (3t - 6)/2 = 252 3t^2 - 6t - 504 = 0 t^2 - 2t - 168 = 0 (t - 14) (t + 12) = 0 t = 14 days the tourist had to go. t - 2 = 12 days the tourist went actually. 2) There had to be an of boxes on b of pieces in each a*b = 378 Esli in each box to put on b+9 of objects, a-1 a box is necessary. (a - 1) (+ 9) = to a*b = 378 a*b - b + 9a - 9 = to a*b b = 9a - 9 a*b = to a (9a - 9) = 378 9a^2 - 9a - 378 = 0 a^2 - a - 42 = 0 (a - 7) (a + 6) = 0 a = 7 boxes are necessary for b, in everyone 378/7 = 54 objects. Esli in each box 54 + 9 = 63 objects, are necessary 378/63 = 6 boxes. 3) In a rack of n of shelves, on everyone on k of books. n*k = 640 Esli for each shelf to deliver to k + 8 books, n - 4 shelves is necessary. (k + 8) (n - 4) = n*k = 640 k*n + 8n - 4k - 32 = n*k k = (8n - 32)/4 = 2n - 8 n (2n - 8) = 640 2n^2 - 8n - 640 = 0 n^2 - 4n - 320 = 0 (n - 20) (n + 16) = 0 n = 20 shelves, on everyone on 640/20 = 32 books. n - 4 = 16 shelves, on everyone on 640/16 = 40 books .

259

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yuri

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