document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193391>Question 1193391</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Raina works as a tutor for $7 an hour and as a waitress for $12 an hour. This month, she worked a combined total of 97 hours at her two jobs.<BR>\n" );
document.write( "Let t be the number of hours Raina worked as a tutor this month. Write an expression for the combined total dollar amount she earned this month. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #825400 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=825400\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = the number of hours worked as a tutor<BR>\n" );
document.write( "let y = the number of hours worked as a waitress.<BR>\n" );
document.write( "let t = the total number of hours she worked during the month.<BR>\n" );
document.write( "7x = the total amount of money she made as a tutor.<BR>\n" );
document.write( "15y = the total amount of money she made as a waitress.<BR>\n" );
document.write( "t = x + y means the total number of hours she worked during the month is the sum of the total number of hours she worked as a tutor plus the total number of hours she worked as a waitress during the month.<BR>\n" );
document.write( "let d = the total amount of dollars she made during the month.<BR>\n" );
document.write( "the formula for d becomes:<BR>\n" );
document.write( "d = 7x + 15y<BR>\n" );
document.write( "that's the equation for the total dollar amount she made during the month.<BR>\n" );
document.write( "the expression to determine the total dollar amount she earned during the month is 7x + 15y.<BR>\n" );
document.write( "that's the expression on the right side of the equation.\r<BR>\n" );
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document.write( "in answer to your request for a numeric solution, please read the following:\r<BR>\n" );
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document.write( "the problem does clearly state to \"Write an expression for the combined total dollar amount she earned this month.\"<BR>\n" );
document.write( "it does not ask for a numeric solution.\r<BR>\n" );
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document.write( "despite that, i don't believe this problem lends itself to a unique solution, the reason being that you have 2 equations in 3 unknowns.<BR>\n" );
document.write( "your 3 unknowns are the number of hours worked at 7 dollars an hour and the number of hours worked at 15 dollars an hour and the total amount of money that was made.<BR>\n" );
document.write( "you do know that the total  hours worked is 97, but  you don't know what the total amount of money that was earned is.<BR>\n" );
document.write( "that is required, as far as i can tell, for there to be unique solution.<BR>\n" );
document.write( "there are limits to the amount of money that can be earned, given the constraints of the problem.<BR>\n" );
document.write( "the minimum money that can be earned is 7 * 97 + 15 * 0 = 679.<BR>\n" );
document.write( "the maximum money that can be earned is 7 * 0 + 15 * 97 = 1455.<BR>\n" );
document.write( "what this says is that she couldn't make less than 679 dollars and she couldn't make more than 1455 dollars, given that she worked 97 hours during the week at 7 dollars an hour for the tutor job and 15 dollars an hour for the waitress job.<BR>\n" );
document.write( "if you pick any amount of money between these extremes, you can then solve for the number of hours worked at each.<BR>\n" );
document.write( "for example, if you say that she made 1000 dollars during the week, then you can solve for the number of hours worked at each job as follows:<BR>\n" );
document.write( "your equations become:<BR>\n" );
document.write( "x + y = 97<BR>\n" );
document.write( "7x + 15y = 1000<BR>\n" );
document.write( "these are 2 equations that need to b solved simultaneously.<BR>\n" );
document.write( "multiply both sides of the first equation by 7 to get:<BR>\n" );
document.write( "7x + 7y = 679<BR>\n" );
document.write( "7x + 15y = 1000<BR>\n" );
document.write( "subtract the first equation from the second to get:<BR>\n" );
document.write( "8y = 321<BR>\n" );
document.write( "solve for y to get:<BR>\n" );
document.write( "y = 321/8 = 40.125.<BR>\n" );
document.write( "since x + y = 97, then y = 97 - 40.125 = 56.875<BR>\n" );
document.write( "to confirm, replace x and y in the original equations to get:<BR>\n" );
document.write( "x + y = 97 becomes 56.875 + 40.125 = 97 which becomes 97 = 97 which is true.<BR>\n" );
document.write( "7x + 15y = 1000 becomes 7*56.875 + 15 * 40.125 = 1000 which becomes 1000 = 1000 which is true.<BR>\n" );
document.write( "if the total amount of money earned is 1000, then the value of x and y will be 56.875 and 40.125 respectively.<BR>\n" );
document.write( "given another value of money earned between 679 and 1455, you would get a different number of hours for x and y.<BR>\n" );
document.write( "let me know if you have any further questions.<BR>\n" );
document.write( "i'll answer to the best of my ability.<BR>\n" );
document.write( "theo\r<BR>\n" );
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