document.write( "Question 269002: How would you work out this problem; It requires to show all work!\r
\n" ); document.write( "\n" ); document.write( "The cafeteria has 360 roses to sell for Valentine's Day. You want to pick
\n" ); document.write( "out a perfect red rose for someone special. When you get to the cafeteria
\n" ); document.write( "you discover:\r
\n" ); document.write( "\n" ); document.write( "*every third rose is too short
\n" ); document.write( "*every fourth rose has too many thorns
\n" ); document.write( "*every fifth rose is wilted
\n" ); document.write( "*every sixth rose is pink
\n" ); document.write( "*every eighth rose is yellow\r
\n" ); document.write( "\n" ); document.write( "If these are the only problems that the roses have, how many perfect roses are
\n" ); document.write( "there for you to choose from?\r
\n" ); document.write( "\n" ); document.write( "The problem requires to show all work. I would think that there is an
\n" ); document.write( "algebraic expression that would help me out, but I am in need of help.
\n" ); document.write( "I can help myself by making pictures to help visualize, but I think there must
\n" ); document.write( "be a better way.\r
\n" ); document.write( "\n" ); document.write( "Please help me if you can. Thank you! \n" ); document.write( "
Algebra.Com's Answer #197150 by drk(1908)\"\" \"About 
You can put this solution on YOUR website!
It seems to me that you count 1, 2 and then primes greater than 5, and multiples of primes. Here is the list that I have:
\n" ); document.write( "1, 2,
\n" ); document.write( "7, 14, 49, 77, 91, 98, 119, . . . . . .. . . . . . .. [22 options]
\n" ); document.write( "11, 22, 121, 143, 154, . . . . . . . . . . . . . . [12 options
\n" ); document.write( "13, 26, 169, 182, 221, 247, 286, 299, 338 [9 options]
\n" ); document.write( "17, 34, 289, 323 . . . . . . . . . . . . . . . . . . . . .[4 options]
\n" ); document.write( "19, 38, 23, 46, 29, 58, 31, 62, 37, 74
\n" ); document.write( "41, 82, 43, 86, 47, 94, 53, 106, 59, 118,
\n" ); document.write( "61, 122, 67, 134, 71, 142, 73, 146, 77, 154,
\n" ); document.write( "79, 158, 83, 166, 89, 178, 91, 182, 97, 194,
\n" ); document.write( "101, 202, 103, 206, 107, 214, 109, 218, 113, 226,
\n" ); document.write( "127, 254, 131, 262, 137, 274, 139, 278, 149, 298,
\n" ); document.write( "151, 302, 157, 314, 163, 326, 167, 334, 173, 346,
\n" ); document.write( "179, 358,
\n" ); document.write( "----
\n" ); document.write( "181, 191, 193, 197, 199, 211, 223, 227, 229, 233,
\n" ); document.write( "239, 241, 251, 257, 263, 269, 271, 277, 281, 283,
\n" ); document.write( "293, 307, 311, 313, 317, 331, 337, 347, 349, 353,
\n" ); document.write( "359
\n" ); document.write( "----
\n" ); document.write( "so our total appears to be: 2 + 22 + 12 + 9 + 4 + 72 + 31 = 152 good options
\n" ); document.write( "---
\n" ); document.write( "On a personal note I didn't like this question. It could have been set up better using a smaller number such as 100 roses. \n" ); document.write( "
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