document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=626199>Question 626199</A>: <I><SPAN STYLE=\"word-break: break-all;\"> my daughter is in year 6 at school and has been given maths homework which i cant help her with i have 2 questions but need to be able to show workings out and be able to understand how we got the answer.\r<BR>\n" );
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document.write( "1) fatma is thinking of a 3 digit odd number. the hundreds digit is 3 times more than the units digit. the sum of the three digits is 4. what number is fatma thinking off\r<BR>\n" );
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document.write( "2)who am i, i have 3 digit i can only be divived by myself and one. the sum of my digits is 11 i am under 150 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #394024 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=394024\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> problem number 1:<BR>\n" );
document.write( "fatma is thinking of a 3 digit odd number. the hundreds digit is 3 times more than the units digit. the sum of the three digits is 4. what number is fatma thinking of \r<BR>\n" );
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document.write( "since the number is odd, the ones digit can only be { 1,3,5,7, or 9 }<BR>\n" );
document.write( "since the hundreds digit has to be 3 times the ones digit, it can only be 3 or 9.<BR>\n" );
document.write( "3 is 3 times 1<BR>\n" );
document.write( "9 is 3 times 3<BR>\n" );
document.write( "since the sum of the digits has to be equal to 4, we get:<BR>\n" );
document.write( "hundreds digit equals 3<BR>\n" );
document.write( "tens digit equals 0<BR>\n" );
document.write( "ones digit equals 1<BR>\n" );
document.write( "the number is 301<BR>\n" );
document.write( "sum of the digits is 4<BR>\n" );
document.write( "hundreds digit is 3 times units digit<BR>\n" );
document.write( "number is odd\r<BR>\n" );
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document.write( "problem number 2:<BR>\n" );
document.write( "who am i, i have 3 digits. i can only be divided by myself and one. the sum of my digits is 11. i am under 150.\r<BR>\n" );
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document.write( "the first digit has to be 1 since the number has to be less than 150.<BR>\n" );
document.write( "the sum of all 3 digits have to be equal to 11<BR>\n" );
document.write( "this means the sum of the tens digits and the ones digit has to be 10 because the hundreds digit has to be 1.<BR>\n" );
document.write( "you have the following options:<BR>\n" );
document.write( "119<BR>\n" );
document.write( "128<BR>\n" );
document.write( "137<BR>\n" );
document.write( "146<BR>\n" );
document.write( "that all since your number has to be below 150.<BR>\n" );
document.write( "128 and 146 can't be the number because they are divisible by 2.<BR>\n" );
document.write( "you are left with 119 or 137<BR>\n" );
document.write( "the number has to be prime (only divisible by itself or 1 means the number is prime).<BR>\n" );
document.write( "both are divisible by 1<BR>\n" );
document.write( "neither is divisible by 2<BR>\n" );
document.write( "neither is divisible by 3<BR>\n" );
document.write( "neither by 4<BR>\n" );
document.write( "neither by 5<BR>\n" );
document.write( "neither by 6<BR>\n" );
document.write( "neither by 7<BR>\n" );
document.write( "neither by 8<BR>\n" );
document.write( "neither by 9<BR>\n" );
document.write( "they look to both be prime.<BR>\n" );
document.write( "i checked the web for prime numbers to see if either one or both was on the list.<BR>\n" );
document.write( "here's the list i got:<BR>\n" );
document.write( "<a hred = \"http://wiki.answers.com/Q/List_of_prime_numbers_up_to_200\" target = \"_blank\">http://wiki.answers.com/Q/List_of_prime_numbers_up_to_200</a><BR>\n" );
document.write( "i know it was cheating, but i didn't feel like going through the drudgery of testing each one.<BR>\n" );
document.write( "from this list, it looks like 137 is the prime number and 119 is not.<BR>\n" );
document.write( "that means that 119 must be divisible by something other than 119 or 1.<BR>\n" );
document.write( "since i'm basically lazy, i enlisted the help of microsoft excel to find the numbers that are divisible into 119.<BR>\n" );
document.write( "the results of that analysis are shown below:<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "			4 (minus 2 = 2)		2 (minus 2 = 0)\r\n" );
document.write( "number is divisible by 1 and divisible by itself so the total number of numbers\r\n" );
document.write( "it is divisible by are the count minus 2.  the count above shows that 119 has\r\n" );
document.write( "2 divisors other than 1 and itself, while 137 has 0 divisors other than 1 and \r\n" );
document.write( "itself. \r\n" );
document.write( "the actual search is below;\r\n" );
document.write( "the first column is the divisor\r\n" );
document.write( "the second column is the number 119 divided by the divisor in column 1.\r\n" );
document.write( "the third column is equal to 1 if the answer is an integer and is equal to\r\n" );
document.write( "0 if the answer is not an integer.\r\n" );
document.write( "the fourth column is the number 137 divided by the divisor in column 1.\r\n" );
document.write( "the fifth column is equal to 1 if the answer is an integer and is equal to \r\n" );
document.write( "0 if the answer is not an integer.\r\n" );
document.write( "						\r\n" );
document.write( "1		119	        1		137	        1\r\n" );
document.write( "2		59.5	        0		68.5	        0\r\n" );
document.write( "3		39.66666667	0		45.66666667	0\r\n" );
document.write( "4		29.75	        0		34.25	        0\r\n" );
document.write( "5		23.8	        0		27.4	        0\r\n" );
document.write( "6		19.83333333	0		22.83333333	0\r\n" );
document.write( "7		17	        1		19.57142857	0\r\n" );
document.write( "8		14.875	        0		17.125	        0\r\n" );
document.write( "9		13.22222222	0		15.22222222	0\r\n" );
document.write( "10		11.9	        0		13.7	        0\r\n" );
document.write( "11		10.81818182	0		12.45454545	0\r\n" );
document.write( "12		9.916666667	0		11.41666667	0\r\n" );
document.write( "13		9.153846154	0		10.53846154	0\r\n" );
document.write( "14		8.5	        0		9.785714286	0\r\n" );
document.write( "15		7.933333333	0		9.133333333	0\r\n" );
document.write( "16		7.4375	        0		8.5625	        0\r\n" );
document.write( "17		7	        1		8.058823529	0\r\n" );
document.write( "18		6.611111111	0		7.611111111	0\r\n" );
document.write( "19		6.263157895	0		7.210526316	0\r\n" );
document.write( "20		5.95	        0		6.85	        0\r\n" );
document.write( "21		5.666666667	0		6.523809524	0\r\n" );
document.write( "22		5.409090909	0		6.227272727	0\r\n" );
document.write( "23		5.173913043	0		5.956521739	0\r\n" );
document.write( "24		4.958333333	0		5.708333333	0\r\n" );
document.write( "25		4.76	        0		5.48	        0\r\n" );
document.write( "26		4.576923077	0		5.269230769	0\r\n" );
document.write( "27		4.407407407	0		5.074074074	0\r\n" );
document.write( "28		4.25	        0		4.892857143	0\r\n" );
document.write( "29		4.103448276	0		4.724137931	0\r\n" );
document.write( "30		3.966666667	0		4.566666667	0\r\n" );
document.write( "31		3.838709677	0		4.419354839	0\r\n" );
document.write( "32		3.71875	        0		4.28125	        0\r\n" );
document.write( "33		3.606060606	0		4.151515152	0\r\n" );
document.write( "34		3.5	        0		4.029411765	0\r\n" );
document.write( "35		3.4	        0		3.914285714	0\r\n" );
document.write( "36		3.305555556	0		3.805555556	0\r\n" );
document.write( "37		3.216216216	0		3.702702703	0\r\n" );
document.write( "38		3.131578947	0		3.605263158	0\r\n" );
document.write( "39		3.051282051	0		3.512820513	0\r\n" );
document.write( "40		2.975	        0		3.425	        0\r\n" );
document.write( "41		2.902439024	0		3.341463415	0\r\n" );
document.write( "42		2.833333333	0		3.261904762	0\r\n" );
document.write( "43		2.76744186	0		3.186046512	0\r\n" );
document.write( "44		2.704545455	0		3.113636364	0\r\n" );
document.write( "45		2.644444444	0		3.044444444	0\r\n" );
document.write( "46		2.586956522	0		2.97826087	0\r\n" );
document.write( "47		2.531914894	0		2.914893617	0\r\n" );
document.write( "48		2.479166667	0		2.854166667	0\r\n" );
document.write( "49		2.428571429	0		2.795918367	0\r\n" );
document.write( "50		2.38	        0		2.74	        0\r\n" );
document.write( "51		2.333333333	0		2.68627451	0\r\n" );
document.write( "52		2.288461538	0		2.634615385	0\r\n" );
document.write( "53		2.245283019	0		2.58490566	0\r\n" );
document.write( "54		2.203703704	0		2.537037037	0\r\n" );
document.write( "55		2.163636364	0		2.490909091	0\r\n" );
document.write( "56		2.125	        0		2.446428571	0\r\n" );
document.write( "57		2.087719298	0		2.403508772	0\r\n" );
document.write( "58		2.051724138	0		2.362068966	0\r\n" );
document.write( "59		2.016949153	0		2.322033898	0\r\n" );
document.write( "60		1.983333333	0		2.283333333	0\r\n" );
document.write( "61		1.950819672	0		2.245901639	0\r\n" );
document.write( "62		1.919354839	0		2.209677419	0\r\n" );
document.write( "63		1.888888889	0		2.174603175	0\r\n" );
document.write( "64		1.859375	0		2.140625	0\r\n" );
document.write( "65		1.830769231	0		2.107692308	0\r\n" );
document.write( "66		1.803030303	0		2.075757576	0\r\n" );
document.write( "67		1.776119403	0		2.044776119	0\r\n" );
document.write( "68		1.75	        0		2.014705882	0\r\n" );
document.write( "69		1.724637681	0		1.985507246	0\r\n" );
document.write( "70		1.7	        0		1.957142857	0\r\n" );
document.write( "71		1.676056338	0		1.929577465	0\r\n" );
document.write( "72		1.652777778	0		1.902777778	0\r\n" );
document.write( "73		1.630136986	0		1.876712329	0\r\n" );
document.write( "74		1.608108108	0		1.851351351	0\r\n" );
document.write( "75		1.586666667	0		1.826666667	0\r\n" );
document.write( "76		1.565789474	0		1.802631579	0\r\n" );
document.write( "77		1.545454545	0		1.779220779	0\r\n" );
document.write( "78		1.525641026	0		1.756410256	0\r\n" );
document.write( "79		1.506329114	0		1.734177215	0\r\n" );
document.write( "80		1.4875	        0		1.7125	        0\r\n" );
document.write( "81		1.469135802	0		1.691358025	0\r\n" );
document.write( "82		1.451219512	0		1.670731707	0\r\n" );
document.write( "83		1.43373494	0		1.65060241	0\r\n" );
document.write( "84		1.416666667	0		1.630952381	0\r\n" );
document.write( "85		1.4	        0		1.611764706	0\r\n" );
document.write( "86		1.38372093	0		1.593023256	0\r\n" );
document.write( "87		1.367816092	0		1.574712644	0\r\n" );
document.write( "88		1.352272727	0		1.556818182	0\r\n" );
document.write( "89		1.337078652	0		1.539325843	0\r\n" );
document.write( "90		1.322222222	0		1.522222222	0\r\n" );
document.write( "91		1.307692308	0		1.505494505	0\r\n" );
document.write( "92		1.293478261	0		1.489130435	0\r\n" );
document.write( "93		1.279569892	0		1.47311828	0\r\n" );
document.write( "94		1.265957447	0		1.457446809	0\r\n" );
document.write( "95		1.252631579	0		1.442105263	0\r\n" );
document.write( "96		1.239583333	0		1.427083333	0\r\n" );
document.write( "97		1.226804124	0		1.412371134	0\r\n" );
document.write( "98		1.214285714	0		1.397959184	0\r\n" );
document.write( "99		1.202020202	0		1.383838384	0\r\n" );
document.write( "100		1.19	        0		1.37	        0\r\n" );
document.write( "101		1.178217822	0		1.356435644	0\r\n" );
document.write( "102		1.166666667	0		1.343137255	0\r\n" );
document.write( "103		1.155339806	0		1.330097087	0\r\n" );
document.write( "104		1.144230769	0		1.317307692	0\r\n" );
document.write( "105		1.133333333	0		1.304761905	0\r\n" );
document.write( "106		1.122641509	0		1.29245283	0\r\n" );
document.write( "107		1.112149533	0		1.280373832	0\r\n" );
document.write( "108		1.101851852	0		1.268518519	0\r\n" );
document.write( "109		1.091743119	0		1.256880734	0\r\n" );
document.write( "110		1.081818182	0		1.245454545	0\r\n" );
document.write( "111		1.072072072	0		1.234234234	0\r\n" );
document.write( "112		1.0625 	        0		1.223214286	0\r\n" );
document.write( "113		1.053097345	0		1.212389381	0\r\n" );
document.write( "114		1.043859649	0		1.201754386	0\r\n" );
document.write( "115		1.034782609	0		1.191304348	0\r\n" );
document.write( "116		1.025862069	0		1.181034483	0\r\n" );
document.write( "117		1.017094017	0		1.170940171	0\r\n" );
document.write( "118		1.008474576	0		1.161016949	0\r\n" );
document.write( "119		1	        1		1.151260504	0\r\n" );
document.write( "120		0.991666667	0		1.141666667	0\r\n" );
document.write( "121		0.983471074	0		1.132231405	0\r\n" );
document.write( "122		0.975409836	0		1.12295082	0\r\n" );
document.write( "123		0.967479675	0		1.113821138	0\r\n" );
document.write( "124		0.959677419	0		1.10483871	0\r\n" );
document.write( "125		0.952	        0		1.096	        0\r\n" );
document.write( "126		0.944444444	0		1.087301587	0\r\n" );
document.write( "127		0.937007874	0		1.078740157	0\r\n" );
document.write( "128		0.9296875	0		1.0703125	0\r\n" );
document.write( "129		0.92248062	0		1.062015504	0\r\n" );
document.write( "130		0.915384615	0		1.053846154	0\r\n" );
document.write( "131		0.908396947	0		1.045801527	0\r\n" );
document.write( "132		0.901515152	0		1.037878788	0\r\n" );
document.write( "133		0.894736842	0		1.030075188	0\r\n" );
document.write( "134		0.888059701	0		1.02238806	0\r\n" );
document.write( "135		0.881481481	0		1.014814815	0\r\n" );
document.write( "136		0.875	        0		1.007352941	0\r\n" );
document.write( "137		0.868613139	0		1	        1\r\n" );
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document.write( "</PRE><BR>\n" );
document.write( "looks like 119 is divisible by 2 numbers.<BR>\n" );
document.write( "those numbers are 7 and 17.<BR>\n" );
document.write( "looks like i missed 7 in my preliminary analysis since, if i had found it then, i would have saved some additional effort down the road.<BR>\n" );
document.write( "119 / 7 = 17<BR>\n" );
document.write( "7 * 17 = 70 + 49 = 119.<BR>\n" );
document.write( "that's it.<BR>\n" );
document.write( "119 is divisible  by 7 or 17.<BR>\n" );
document.write( "your answer has to be 137.\r<BR>\n" );
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document.write( "there was not a formula you could used other than logic.<BR>\n" );
document.write( "i tried using a formula in the first problem but it didn't really help much.<BR>\n" );
document.write( "it was the logic of numbers and digits and what they could be or not be that led to the solution.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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