document.write( "Question 1202710: The ratio of boys to girls among the students who signed up for a basketball competition is 4:3. If 3 boys drop out of the competition and 4 girls join, there will be the same number of boys and girls. Evaluate the number of students who signed up for the basketball competition. \n" ); document.write( "

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document.write( "The ratio of boys to girls among the students who signed up for a basketball competition is 4:3. If 3 boys drop out of the competition and 4 girls join, there will be the same number of boys and girls. Evaluate the number of students who signed up for the basketball competition.\r\n" );
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document.write( "Let the multiplicative factor for the number of students who signed up, be x\r\n" );
document.write( "As the ratio of boys to girls who signed up was 4:3, number of boys who signed up was 4x, and\r\n" );
document.write( "number of girls, 3x, which makes the total number of students who signed up, 4x + 3x = 7x\r\n" );
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document.write( "With 3 boys dropping out, 4x - 3 remained. And, with 4 girls joining, number of girls became 3x + 4\r\n" );
document.write( "As the number of boys and girls, then, was the same, then the NEW ratio now equals 1. \r\n" );
document.write( "We then have: \r\n" );
document.write( "               4x - 3 = 3x + 4 ----- Cross-multiplying\r\n" );
document.write( "              4x - 3x = 4 + 3\r\n" );
document.write( "Multiplicative factor for the number of students who signed up, or x = 7\r\n" );
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document.write( "Total number of students who signed up: 7x = 7(7) = 49

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