document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1173934>Question 1173934</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find how many numbers are between  1 and 2019 , such that number is a multiple of 5 and contains digit 5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #799272 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=799272\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "You learn nothing, and your brain gets no exercise, from our doing this problem for you.<br><BR>\n" );
document.write( "So I will show you an organized way to do the counting and let you find the answer.<br><BR>\n" );
document.write( "Note there is no magic formula that will find this answer for you.<br><BR>\n" );
document.write( "You could write a computer program to find the answer; and writing that program would be an excellent exercise.  But that is not what they want you to do.<br><BR>\n" );
document.write( "But other than that, the way to find the answer is to find an organized way to count the numbers so that you count each one once and only once.<br><BR>\n" );
document.write( "Numbers that are multiples of 5 have units digit either 5 or 0.  Split the process of counting the numbers you are looking for into those two cases.<br><BR>\n" );
document.write( "(1) Numbers 1 ... 2019 with units digit 5: 5, 15, 25, ..., 2015.  Count them.<br><BR>\n" );
document.write( "(2) Numbers 1 ... 2019 with units digit 0 and some digit 5....<br><BR>\n" );
document.write( "(2a) Numbers with 5 in the tens place and 0 in the units place: count them<BR>\n" );
document.write( "(2b) Numbers with 5 in the hundreds place and 0 in the units place: count them<BR>\n" );
document.write( "(2c) Numbers with 5 in BOTH the tens place and hundreds place: count them<br><BR>\n" );
document.write( "The numbers with 0 in the units place and 5 in both the tens and hundreds places were counted twice in steps (2a) and (2b).  So those numbers, counted in step (2c), must be subtracted from the total.<br><BR>\n" );
document.write( "The answer to the problem is then the numbers from<br><BR>\n" );
document.write( "(1) + ((2a)+(2b)) - (2c)<br><BR>\n" );
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