document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207595>Question 1207595</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi<BR>\n" );
document.write( "At a carnival the ratio of females to males was 7 to 10 . The ratio of men to boys was 5 to 4. The ratio of women to girls was 5 to 4.<BR>\n" );
document.write( "What fraction were children. <BR>\n" );
document.write( "If there were 450 more men than women how many males were at the carnival.  </SPAN>\n" );
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document.write( "The ratio of females to males was 7 to 10:<BR>\n" );
document.write( "Let 7x = # of females<BR>\n" );
document.write( "Let 10x = # of males<br><BR>\n" );
document.write( "The ratio of men to boys was 5 to 4:<BR>\n" );
document.write( "Let 5y = # of men<BR>\n" );
document.write( "Let 4y = # of boys<br><BR>\n" );
document.write( "The number of males is equal to the number of men plus the number of boys:<BR>\n" );
document.write( "5y+4y = 10x<br><BR>\n" );
document.write( "To avoid having to work with ugly fractions, \"scale up\" the definitions of the numbers of men and boys so that the sum is a multiple of 10:<BR>\n" );
document.write( "Let 50y = # of men<BR>\n" );
document.write( "Let 40y = # of boys<br><BR>\n" );
document.write( "Now the number of males is 50y+40y = 90y.<br><BR>\n" );
document.write( "The number of males is 90y; and the number of females is 7/10 of the number of males.  So the number of females is 7/10 of 90y, which is 63y.<br><BR>\n" );
document.write( "The ratio of women to girls was 5 to 4:<BR>\n" );
document.write( "Let 5z = # of women<BR>\n" );
document.write( "Let 4z = # of girls<br><BR>\n" );
document.write( "The number of females (63) is the sum of the numbers of women and girls:<BR>\n" );
document.write( "5z+4z=63y<BR>\n" );
document.write( "9z=63y<BR>\n" );
document.write( "z=7y<br><BR>\n" );
document.write( "The number of women was 5z=35y; the number of girls was 4z=28y.<br><BR>\n" );
document.write( "We now have....<BR>\n" );
document.write( "# of men = 50y<BR>\n" );
document.write( "# of boys = 40y<BR>\n" );
document.write( "# of women = 35y<BR>\n" );
document.write( "# of girls = 28y<br><BR>\n" );
document.write( "First question -- what fraction of the people were children?<br><BR>\n" );
document.write( "# of children = 40y+28y = 68y<BR>\n" );
document.write( "# of people = 50y+40y+35y+28y=153y<BR>\n" );
document.write( "fraction of the people that were children: 68y/153y = 68/153 = 4/9<br><BR>\n" );
document.write( "ANSWER: 4/9 of the people were children<br><BR>\n" );
document.write( "Second question -- If there were 450 more men than women how many males were at the carnival?<br><BR>\n" );
document.write( "The number of men was 450 more than the number of women:<BR>\n" );
document.write( "50y-35y=450<BR>\n" );
document.write( "15y=450<BR>\n" );
document.write( "y=30<br><BR>\n" );
document.write( "# of males = 90y = 90*30 = 2700<br><BR>\n" );
document.write( "ANSWER: There were 2700 males at the carnival<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );