document.write( "Question 826543: From a group of boys and girls, 14 girls leave first. Then the ratio of the number of girls to the number of boys becomes 1:2. After this, 43 boys leave the group. Now the boys and girls are equal in number. How many girls were there in the beginning? \n" ); document.write( "
Algebra.Com's Answer #498194 by ankor@dixie-net.com(22740)![]() ![]() You can put this solution on YOUR website! From a group of boys and girls, 14 girls leave first. \n" ); document.write( " Then the ratio of the number of girls to the number of boys becomes 1:2. \n" ); document.write( " After this, 43 boys leave the group. \n" ); document.write( " Now the boys and girls are equal in number. \n" ); document.write( " How many girls were there in the beginning? \n" ); document.write( ": \n" ); document.write( "Let g = no. of girls originally \n" ); document.write( "let b = no. of boys originally \n" ); document.write( ": \n" ); document.write( "\"From a group of boys and girls, 14 girls leave first. \n" ); document.write( " Then the ratio of the number of girls to the number of boys becomes 1:2. \n" ); document.write( " \n" ); document.write( "Cross multiply \n" ); document.write( "1b = 2(g-14) \n" ); document.write( "b = 2g - 28 \n" ); document.write( ": \n" ); document.write( "\" After this, 43 boys leave the group. \n" ); document.write( " Now the boys and girls are equal in number.\" \n" ); document.write( "b - 43 = g - 14 \n" ); document.write( "b = g - 14 + 43 \n" ); document.write( "b = g + 29 \n" ); document.write( "Replace b with (2g-28) \n" ); document.write( "2g - 28 = g + 29 \n" ); document.write( "2g - g = 29 + 28 \n" ); document.write( "g = 57 girls originally \n" ); document.write( ": \n" ); document.write( ": \n" ); document.write( "We can confirm this by finding the no. of boys \n" ); document.write( "b = 2(57) - 28 \n" ); document.write( "b = 86 boys \n" ); document.write( " |