document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198920>Question 1198920</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm saving money over a year in order to buy a $157.50 gift. I start with an empty piggy bank. In January I put in a small amount of money. Each month after January, I put in $1.75 more than I put in the previous month. By the end of December, I've saved $157.50 exactly. The amount in dollars that I had in my piggy bank after April's deposit was </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832589 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=832589\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The amounts put in the piggy bank in each month form an arithmetic sequence with a common difference of 1.75.<br><BR>\n" );
document.write( "The sum of the terms of an arithmetic sequence is<br><BR>\n" );
document.write( "(number of terms) times (average of the terms)<BR>\n" );
document.write( "= (number of terms) times (average of first and last terms)<BR>\n" );
document.write( "= (number of terms) times ((first plus last)/2)<BR>\n" );
document.write( "= (half the number of terms) times (first plus last)<br><BR>\n" );
document.write( "The sum of the 12 terms for the 12 months is the final amount, 157.50, so<br><BR>\n" );
document.write( "6(first plus last) = 157.50<BR>\n" );
document.write( "first plus last = 157.50/6 = 26.25<br><BR>\n" );
document.write( "The sum of the 6th and 7th terms is the same as the sum of the first and last; and the difference between the 6th and 7th terms is 1.75.  Let x and y be the amounts put in the piggy bank in the 6th and 7th months; then<br><BR>\n" );
document.write( "y+x=26.25<BR>\n" );
document.write( "y-x=1.75<BR>\n" );
document.write( "2y=28<BR>\n" );
document.write( "y=14<br><BR>\n" );
document.write( "The amount put in the piggy bank in the 7th month (July) was $14.<br><BR>\n" );
document.write( "The amount put in the piggy bank in the first month was $14, minus the common difference of $1.75 6 times: $14-6($1.75) = $14-$10.50 = $3.50.<br><BR>\n" );
document.write( "The amounts put in the piggy bank in each month were then<br><BR>\n" );
document.write( "$3.50, $5.25, $7, $8.75, $10.50, $12.25, $14, $15.75, $17.50, $19.25, $21, and $22.75<br><BR>\n" );
document.write( "The amount in the piggy bank after April's deposit was<br><BR>\n" );
document.write( "ANSWER: $3.50 + $5.25 + $7 + $8.75 = $24.50<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );