document.write( "Question 1176916: Hi
\n" ); document.write( "The ratio of teachers to boys to girls is 3:6:4 respectively. The ratio of girls to male teachers is 3:1 respectively. If there were 65 female teachers, how many boys are in the school.
\n" ); document.write( "Thanks
\n" ); document.write( "

Algebra.Com's Answer #805089 by ankor@dixie-net.com(22740)\"\" \"About 
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\n" ); document.write( "The ratio of teachers to boys to girls is 3:6:4 respectively.
\n" ); document.write( "let x = the multiplier
\n" ); document.write( "then
\n" ); document.write( "3x = no. of teachers
\n" ); document.write( "6x = no. of boys
\n" ); document.write( "4x = no. of girls
\n" ); document.write( "let m = no. of male teachers
\n" ); document.write( " The ratio of girls to male teachers is 3:1 respectively.
\n" ); document.write( "\"%284x%29%2Fm\" = \"3%2F1\"
\n" ); document.write( "Cross multiply
\n" ); document.write( "4x = 3m
\n" ); document.write( "m = \"4%2F3\"x
\n" ); document.write( "If there were 65 female teachers, how many boys are in the school.
\n" ); document.write( "3x = (m+65)
\n" ); document.write( "Replace m with \"4%2F3\"x
\n" ); document.write( "3x = \"4%2F3\"x + 65
\n" ); document.write( "get rid of the fraction, multiply by 3
\n" ); document.write( "9x = 4x + 195
\n" ); document.write( "9x - 4x = 195
\n" ); document.write( "5x = 195
\n" ); document.write( " x = 195/5
\n" ); document.write( " x = 39 is the multiplier
\n" ); document.write( ":
\n" ); document.write( "Find the no. of boys
\n" ); document.write( "6*39 = 234 boys
\n" ); document.write( ";
\n" ); document.write( ":
\n" ); document.write( "Confirm this, find the no. of teachers, girls, and male teachers
\n" ); document.write( "3(39)= 117 teachers
\n" ); document.write( "4(39)= 156 girls
\n" ); document.write( "\"4%2F3\" * 39 = 52 male teachers
\n" ); document.write( ":
\n" ); document.write( "52 + 65 = 117 total teachers
\n" ); document.write( ":
\n" ); document.write( "Find the ratio of girls to male teachers
\n" ); document.write( "\"156%2F52\" = 3
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