document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190070>Question 1190070</A>: <I><SPAN STYLE=\"word-break: break-all;\"> to make omelette , 50 gram of butter and 4 to 6 eggs are needed . the mass of each egg is 70 grams , to the nearest 10 gram , but the mass of butter is exact .<BR>\n" );
document.write( "a) what is the least possible mass of each egg ?<BR>\n" );
document.write( "b)  between what limit does mass , m grams of omelette lie ? </SPAN>\n" );
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document.write( "Part (a)\r<BR>\n" );
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document.write( "The mass of each egg is 70 grams, when rounded to the nearest tens place value.\r<BR>\n" );
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document.write( "Before rounding, the possible mass of each egg (call it x) is on this interval <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=65+%3C=+x+%3C+75 ALIGN=MIDDLE  ALT=\"65+%3C=+x+%3C+75\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The 65 rounds up to 70, but the 75 doesn't round to 70 (it instead rounds to 80), so we exclude 75 from the group.\r<BR>\n" );
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document.write( "The least possible mass of each egg is 65 grams.\r<BR>\n" );
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document.write( "Part (b)\r<BR>\n" );
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document.write( "m = the mass of the omelette in grams\r<BR>\n" );
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document.write( "When considering the smallest mass of each egg (65) and having the lowest number of eggs (4), we'll have 4*65 = 260 grams from the eggs alone. Then add on the mass for the butter (50) and we get 260+50 = 310 grams. This is the lowest m can get. <BR>\n" );
document.write( "We can write either <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+%3E=+310 ALIGN=MIDDLE  ALT=\"m+%3E=+310\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=310+%3C=+m ALIGN=MIDDLE  ALT=\"310+%3C=+m\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "On the opposite side of the spectrum, if we consider x = 75 grams per egg and use 6 eggs, then 75*6 = 450 grams are from the eggs alone. However, keep in mind that we cannot actually reach this upper bound since x itself cannot be 75. <BR>\n" );
document.write( "So more accurately the x < 75 leads to 6x < 450\r<BR>\n" );
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document.write( "Then we add on the 50 grams of butter<BR>\n" );
document.write( "6x < 450<BR>\n" );
document.write( "6x+50 < 450+50<BR>\n" );
document.write( "6x+50 < 500<BR>\n" );
document.write( "m = 6x+50 is smaller than 500 grams\r<BR>\n" );
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document.write( "To summarize the possible range of m, we have this compound inequality<BR>\n" );
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document.write( "m is somewhere between 310 and 500<BR>\n" );
document.write( "m = 310 is possible, but m = 500 is not possible<BR>\n" );
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