document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1121103>Question 1121103</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Susie buys 2 pieces of salmon, each weighing x pounds, and 1 piece of trout,y pounds, where x and y are integers. The salmon costs $3.50 per pound and the trout costs $5 per pound. If the total cost of the fish was $77, what could be the value of y? </SPAN>\n" );
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document.write( "The amount spent on salmon is 7x; the amount spent on trout is 5y.  The total amount spent is 77:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%2B5y+=+77 ALIGN=MIDDLE  ALT=\"7x%2B5y+=+77\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Very informally....<br><BR>\n" );
document.write( "Since x and y are positive integers, 7x is a multiple of 7.  Then, since 77 is a multiple of 7, 5y must also be a multiple of 7.<br><BR>\n" );
document.write( "Since 5 is not a multiple of 7, y must be.  So the possible values of y are 7, 14, 21, ....<br><BR>\n" );
document.write( "But y has to be less than 77/5 = 15.4; so the only two possible values for y are 7 and 14.<br><BR>\n" );
document.write( "Answer: The two possible values for y are 7 and 14.<br><BR>\n" );
document.write( "The same solution, using formal mathematics....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%2B5y+=+77 ALIGN=MIDDLE  ALT=\"7x%2B5y+=+77\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5y+=+77-7x ALIGN=MIDDLE  ALT=\"5y+=+77-7x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5y+=+7%2811-x%29 ALIGN=MIDDLE  ALT=\"5y+=+7%2811-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Since 5 is not a multiple of 7, y must be.<br><BR>\n" );
document.write( "Then, as above, the constraints on the value of y lead to exactly two possible values of y -- 7 and 14.<BR>\n" );
document.write( " </SPAN>\n" );
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