Question 1202710
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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.

Let the multiplicative factor for the number of students who signed up, be x
As the ratio of boys to girls who signed up was 4:3, number of boys who signed up was 4x, and
number of girls, 3x, which makes the total number of students who signed up, 4x + 3x = 7x

With 3 boys dropping out, 4x - 3 remained. And, with 4 girls joining, number of girls became 3x + 4
As the number of boys and girls, then, was the same, then the NEW ratio now equals 1. 
We then have: {{{matrix(1,3, (4x - 3)/(3x + 4), "=", 1)}}}
               4x - 3 = 3x + 4 ----- Cross-multiplying
              4x - 3x = 4 + 3
Multiplicative factor for the number of students who signed up, or x = 7

<font color = red><font size  = 4><b>Total number of students who signed up:</font></font></b> 7x = 7(7) = <font color = red><font size  = 4><b>49 </font></font></b></pre>