Johnny found that the large ones totaled 30 more than three times the number of small ones. The ratio of the?
961063
let # of large ones = x and # of small ones = y\n\nthen x = 30+3y\nand x=6y\n \n=> 6y = 30 + 3y\n=> 3y = 30 \n=> y = 10\n\nand x = 6*10 = 60
421086
At the end there are 8 x 13 = 104 guppies.\nHalf of it came from Benny. Then Alice had 52\nBefore she had 11 more.\nSo she started with 52 + 11 = 63 guppies.
930557
Either we have BBBGGG or GGGBBB. In both cases, there are 3! ways of arranging boys, and 3! ways of arranging girls. So 3!*3!*2 = 72.
693178
60 to 40 = 3 to 2\n\nsolution:\n\n60 / 2 = 30 / 10 = 3\n------------------------------ or 3:2 \n40 / 2 = 20 / 10 = 2\n\n\n300 to 70 = 30 to 7\n\nsolution:\n\n300 / 10 = 30   \n----------------------- or 30:7 \n 70 / 10 =  7
947340
a) 72*60*24*30=3110400\nb) 3110400*12 = 37324800\nc) 37324800*72=...................................... :))
1065929
30% = .3\n2711 X .3 = 813.3\n20% = .2\n2711 X .2 = 542.2
460144
10 own their own computer... if the ratio is 2:1 in favor of the one´s that don´t have it, then 20 don´t have computer, 10 do have it. 20 + 10 = 30 students.
1102914
10\nThey are factors of 60 (in order from largest to smallest).
792528
Do a prime factorization of each number:\n\n18 = 2 x 3 x 3\n30 = 2 x 3 x 5\n42 = 2 x 3 x 7\n\nThe prime factors they have in common are a two (2) and a three (3).\n\n2 x 3 = 6\n\nGCF(18, 30, 42) = 6
412968
70\n\ndivide 30 by a half equals 60
761367
Around a thousand or more.
50183
Form fractions with the ratio, both 3/7 and 7/3.  To "enlarge" multiply by the ratio that will make 27 larger (7/3) to make smaller multiply 27 by the ratio that will make it smaller (3/7).\n\n27 x 7/3 = 9 x 7 = 63 (which can be done in your head).
283770
This is about Ramsy numbers , R(17,3)=3.\nThis is a famous problem, but the proff is not easy.
973961
a) i +(1/3)(j-i)\n\n  b)  \n1-12 =>1-4 & 5-12\n\n... 1-4=>1 & 3-4\n.......3-4=>3 & 4\n\n...5-12=> 5-6 & 7-12\n......5-6=> 5 & 6\n......7-12=>7-8 & 9-12\n..........7-8=>7 & 8\n..........9-12=> 9 & 10-12\n...............10-12=>10 & 11-12\n....................11-12=>11 & 12\n\n c) 1/3 of the computations lead to a subset of the previous set\nwhich is 1/2 the size of the other subset which is lead to twice\nas often. So it averages out to the same number of\ncomputations as a conventional binary search.
166662
12!/3!3!3!3! = 12x11x10x8x7x5.\n\nYou are partitioning a set of n objects into 4 subsets of 3 objects each.\n\nIn general case, when you partion a set of n objects into sets of size a,b,c,d,...  where a + b + c + ... = n, the number of ways to do it is: n!/a!b!c!d!...
809410
250,000 x .063 = 15,750
25183
30 billion / 300 million = $100\n\nThat's all he could give. Close enough, though.