document.write( "Question 1190436: the ratio of the number of boys to the number of girls in a school hall was 8:3 at first. Then 45 more girls joined the students in the hall and there was an equal number of boys and girls. How many children were in the hall in the end? \n" ); document.write( "
Algebra.Com's Answer #822047 by math_tutor2020(3817)\"\" \"About 
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\n" ); document.write( "The ratio 8:3 means we have 8 boys for every 3 girls
\n" ); document.write( "It scales up to 8x:3x for some positive whole number x.\r
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\n" ); document.write( "\n" ); document.write( "8x = number of boys
\n" ); document.write( "3x = number of girls\r
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\n" ); document.write( "\n" ); document.write( "Now we add 45 more girls to get 3x+45 girls overall
\n" ); document.write( "We have an equal amount of both genders, so
\n" ); document.write( "8x = 3x+45
\n" ); document.write( "8x-3x = 45
\n" ); document.write( "5x = 45
\n" ); document.write( "x = 45/5
\n" ); document.write( "x = 9\r
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\n" ); document.write( "\n" ); document.write( "This leads to
\n" ); document.write( "8x = 8*9 = 72 boys
\n" ); document.write( "3x = 3*9 = 27 girls
\n" ); document.write( "before the extra 45 girls enter the hall\r
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\n" ); document.write( "\n" ); document.write( "The ratio 72:27 reduces to 8:3 when you divide both parts by the GCF 9. This helps confirm we have the correct values.\r
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\n" ); document.write( "\n" ); document.write( "Now add 45 to the 27 initial group of girls
\n" ); document.write( "27+45 = 72
\n" ); document.write( "This further helps confirm the correct values earlier.\r
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\n" ); document.write( "\n" ); document.write( "Therefore, there are 72+72 = 144 students\r
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\n" ); document.write( "\n" ); document.write( "Answer: 144
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